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This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains R ⊂ R d , where d ≤ 3. Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations. Error bounds are investigated across different scenarios, including comparisons between the semi-discrete and exact solutions, as well as between the semi-discrete and fully-discrete solutions, along with the fully-discrete and exact solutions. An effective algorithm has been proposed to solve the nonlinear system resulting from the fully-discrete finite element approximation at each time step. The paper also provides computed numerical error results and showcases a variety of numerical experiments to further illustrate and support the findings. [ABSTRACT FROM AUTHOR]

This paper studies the leader–follower consensus problem for nonlinear multi-agent systems with actuator saturation by adaptive event-triggered scheme. This adaptive mechanism allows parameters in triggered mechanism to change automatically compared to fixed ones in traditional strategies. The paper introduces two distinct approaches to address the issue of saturation. The first approach is sector bounded condition, while the second relies on convex hull representation. Compared with the former one, the latter one can reduce the conservatism of controller design effectively. Furthermore, it is assumed that the nonlinear function adheres to incremental quadratic limitations, thereby offering a more comprehensive depiction of its nonlinear properties. Finally, the validity of the proposed approaches is demonstrated by one numerical example in the background of mechanical systems. • The leader–follower consensus problem for nonlinear multi-agent systems with actuator saturation is studied. • Adaptive event-triggered mechanism for multi-agent systems is considered. • Two methods for dealing with saturation are proposed, one is sector bounded condition and another is convex hull representation. • The nonlinear function is supposed to satisfy incremental quadratic constraints. [ABSTRACT FROM AUTHOR]

This paper mainly studies the consensus control strategy for a novel heuristic nonlinear multi-agent system. Compared with most existing related researches, firstly, the novel heuristic nonlinear multi-agent system has the ability to construct its communication network topology heuristically, and can withstand long-term DOS(Denial of Service) attacks, with the advantages of high practicality and security. Secondly, in order to control the multi-agent system, a control protocol based on both saturation effect and impulse control mechanism is studied, which has the advantages of high efficiency, low cost and wide applicability. Thirdly, for the multi-agent system, its dynamic model is constructed and analyzed by Lyapunov stability theory and matrix measure theory, and some sufficient conditions for achieving consensus are obtained. Finally, through two simulation experiments and some corresponding comparative analysis, the correctness, efficiency, and superiority of the theories proposed in this paper were verified. • A "heuristic communication network topology generation rule" is designed. It can scientifically solve the problem of the lack of specific design rules for communication connection among different individuals. • A "saturation impulse control protocol" is designed. It has advantages such as high efficiency and low cost. • This paper constructs a novel nonlinear dynamic model for the multi-agent system, which can withstand long-term DOS attacks. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence solutions to nonlinear Fučík problems of the form (1) A x = α x + − β x − + g (x) , where A is a symmetric n × n matrix, α , β are real numbers, and g : R n → R n is continuous. The nonlinear problem (1) is motivated by application to nonlinear oscillating systems such as the Tacoma Narrows Bridge. The paper begins by developing a qualitative picture of Fučík spectrum associated with the matrix equation A x = α x + − β x −. In this setting, we present two characterizations: first, we show that under appropriate assumptions the Fučík spectrum consists of curves bifurcating from points (λ , λ) ∈ R 2 , where λ is an eigenvalue of A ; second, we give more global variational characterization of the Fučík curves. In both cases, we present various qualitative properties of the Fučík curves. The paper finishes by presenting two existence theorems for the nonlinear Fučík problem under mild assumptions on the nonlinear term g. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional-order time-varying sliding mode control method with predefined-time convergence for a class of arbitrary-order nonlinear control systems with compound disturbances. The method has global robustness and strongly predefined-time stability. All state errors of the system can converge to zero at a desired time, which can be set arbitrarily with a simple parameter. The strongly predefined-time convergence of the system is clearly demonstrated by the analytic expression of state error, which is obtained by solving fractional-order differential equations corresponding to the sliding mode function. The simulation results show that the proposed method still has good control performance in the presence of input saturation and external interference. • The main contributions of this paper are summarized as follows: • A predefined-time fractional-order time-varying sliding mode control scheme is proposed for a class of arbitrary order nonlinear control systems with complex disturbances. All state errors are simultaneously converged to zero by the scheme at a time, which can be presented by a simple parameter. • Different from most of the existing methods, this paper obtains the analytical expression of the state errors by solving the fractional-order differential equation to prove the predefined-time convergence of the system. • The fractional-order term and time-varying term are introduced into the proposed control scheme, which improves the control performance and makes the system have global robustness. The simulation results show that the proposed controller has strong robustness and resistance to input saturation. [ABSTRACT FROM AUTHOR]

The research investigates the fixed-time command-filtered composite adaptive neural fault-tolerant (FCCANF) control issue of strict-feedback nonlinear systems (SFNSs). There exist unknown functions and bounded disturbances in the considered systems. Radial basis function neural networks (RBFNNs) will be used in the estimate of the unknown functions. By the serial–parallel estimation models (SPEMs), the forecast biases and the track biases can change the weights of RBFNNs and the approximate characteristics of RBFNNs will be improved. Then, utilizing the novel fixed-time command filter and adaptive disturbance observers, the issue of complex explosion will be effectively solved and the external disturbance is effectively compensated. Subsequently, by utilizing the adaptive control technique, a novel FCCANF controller is developed. Additionally, we have that the system internal variables are bounded and the output variable inclines to a little interval around zero in fixed time which is not determined by the system initial variables. Eventually, numerical and practical examples are shown to prove the availability of the obtained control technique. • For the paper [23], a second-order fixed-time command filter with the symbolic function is introduced to estimate the derivatives of the virtual controllers. However, in this manuscript, a first-order fixed-time command filter with the smooth hyperbolic tangent function is designed to estimate the derivatives of the virtual controllers. Then, the compensation of filtering errors is not considered in the paper [23]. However, in this manuscript, the compensation of filtering errors is considered. • To improve the RBFNN approximation, the novel fixed-time convergence SPEMs are created and it is the first time to use the matrix element technique to solve the fixed-time patchwork problems for the adaptive laws. Then, to estimate the lumped disturbance, the fixed-time convergence adaptive neural disturbance observers are utilized firstly. • Compared with the papers [22] and [24], based on [25], the hyperbolic tangent functions are introduced to solve the singular problem. [ABSTRACT FROM AUTHOR]

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness. • A novel event-triggered optimal tracking control framework is proposed. • A phenomenon we defined as the "jump of error surfaces" is noticed and tackled via filter technique. • A multi-error based adaptive triggering rule is established to improve the control performance. • The proposed method not only achieves the optimality but also lowers data transmission. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov–Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method. [ABSTRACT FROM AUTHOR]

This paper tackles the event-triggering filtering problem for a class of nonlinear networked control systems subject to the prescribed disturbance attenuation level. To alleviate the data transmission burden of communication channels, an event-triggering mechanism is adopted, where the data can be transmitted only if certain condition is fulfilled. The T-S fuzzy model approach is utilized to approximate the nonlinear dynamics. It is the purpose of this paper to design a filter for the addressed nonlinear system ensuring that the filtering error system is asymptotically stable whereas the prespecified H ∞ criterion is guaranteed. By using Lyapunov approach in combination with matrix analysis method, the sufficient conditions are established for the existence of desired filtering parameters in terms of the solvability of certain linear matrix inequalities. Finally, a numerical simulation example is put forward to demonstrate the validity and effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the robust cooperative output regulation problem for heterogeneous lower triangular nonlinear multi-agent systems with an unknown exosystem over jointly connected switching networks. The problem has been studied for the exactly known exosystem over switching networks. However, the existing result for the unknown exosystem is still limited to the static networks. To ensure that all followers acquire the reference trajectory generated by the unknown exosystem through the jointly connected switching networks, by combining a set of auxiliary filtering variables and fixed-time stability theory, an adaptive distributed observer is designed. On the basis of the adaptive distributed observer and the distributed internal model approach, we propose a distributed controller under several standard assumptions to solve the problem. Compared with the similar work subject to the static networks, the controller in this paper is applicable to the more general communication network while weakening the assumptions of the controlled system. • A new distributed observer is designed for relatively general exosystem and networks. • We transform an unknown exosystem into a known exosystem in a fixed time. • We avoided the additional assumptions of articles studying similar exosystems. • We extended similar articles to more general networks and controlled objects. [ABSTRACT FROM AUTHOR]

Unknown measurement disturbances and correlated noise caused by jitter or vibration phenomena during spacecraft operation and the complex external environment are important topics for spacecraft attitude estimation. This paper studies the problem of spacecraft attitude estimation for nonlinear systems with multiplicative noises, unknown measurement disturbances and correlated noises. In addition, a two-step prediction framework is used to complete the noise decoupling. This paper aims to design a robust filter that minimizes the upper bound of the prediction error covariance and estimation error covariance in the presence of multiplicative noises, correlated noises and unknown measurement disturbances. The prediction gain and filtering gain of the robust filter are designed to minimize the upper bound. Finally, the simulation results verify the effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]

• This paper investigates the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems. • Both cases of stable/unstable continuous dynamics and impulses are studied by unified ADT conditions. • The Lyapunov functions with time-varying linear/nonlinear rates are utilized to handle the twofold effect of impulses. • It determines that the stable nonlinear systems are robust against hybrid impulses with multiple jump maps. In this paper, we investigate the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems involving hybrid impulses which have time-dependent multiple jump maps. Under unified average dwell-time conditions, several criteria for finite-time and fixed-time input-to-state stability are established by virtue of the Lyapunov function with linear rate and nonlinear rate of jump maps. It shows that, when the finite/fixed-time input-to-state stable continuous systems are subject to hybrid impulses, the finite-time and fixed-time input-to-state stability can be ascertained under the requirement that the accumulative effect of hybrid impulses is non-destabilizing or the accumulative effect of hybrid impulses is destabilizing and the impulses are not activated too frequently. Finally, the effectiveness of theoretical results is verified by two numerical examples and an application example about an axisymmetric circular spacecraft. [ABSTRACT FROM AUTHOR]

• Motion planning of a spin-rolling sphere on a plane. • A novel geometric path planning approach with a Darboux frame parametrization. • Planning the spin-rolling sphere on the shortest path on the plane. • Evaluation of the capabilities and performance of the approach in the simulation. The paper deals with motion planning for a spin-rolling sphere when the sphere follows an optimal straight path on a plane. Since the straight line constrains the sphere's motion, controlling the sphere's spin motion is essential to converge to a desired full configuration of the sphere. In this paper, we show a new geometric-based planning approach that is based on a full-state description of this nonlinear system. First, the problem statement of the motion planning is posed. Next, we develop a geometric controller implemented as a virtual surface by using the Darboux frame kinematics. This virtual surface generates arc-length-based inputs for controlling the trajectories of the sphere. Then, an iterative algorithm is designed to tune these inputs for the desired configurations. Finally, the feasibility of the proposed approach is verified by simulations. [ABSTRACT FROM AUTHOR]

An optimization algorithm is presented in this paper for the minimal robust positively invariant (mRPI) set approximations via sums-of-squares (SOS) optimization. The mRPI set is an effective tool for robust analysis of uncertain systems under bounded disturbances. The approximation of the mRPI set is always characterized by a polyhedron computed after finite time iterations. In this paper, an mRPI set is characterized by an ellipsoidal set while bounded parametric uncertainties act on states. The proposed algorithm optimizes the shape matrix of the ellipsoidal set approximation by minimizing the volume of the ellipsoidal set. The algorithm is designed for discrete-time and continuous-time nonlinear systems respectively. The algorithm has the ability to further minimize the mRPI set by optimizing the state-feedback control law. Examples are employed to validate the effectiveness of the proposed algorithms. • A less conservative approach for approximating the mRPI set of the continuous-time system. • A less conservative approach for approximating the mRPI set of the discrete-time system. • A feedback control optimization approach via minimizing the volume of the mRPI set for the continuous-time system. • A feedback control optimization approach via minimizing the volume of the mRPI set for the discrete-time system. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology to obtain prediction regions of the output of a dynamical system. The proposed approach uses stored past outputs of the system and it is entirely data-based. Only two hyperparameters are necessary to apply the proposed methodology. These scalars are chosen so that the size of the obtained regions is minimized while fulfilling the desired empirical probability in a validation set. In this paper, methods to optimally estimate both hyperparameters are provided. The provided prediction regions are convex and checking if a given point belongs to a computed prediction region amounts to solving a convex optimization problem. Also, approximation methods to build ellipsoidal prediction regions are provided. These approximations are useful when explicit descriptions of the regions are necessary. Finally, some numerical examples and comparisons for the case of a non-linear uncertain kite system are provided to prove the effectiveness of the proposed methodology. • A method to compute prediction regions for multivariate systems is presented. • These regions contain future values of the outputs with a certain probability. • The proposed method does not need any knowledge of the system dynamics. • A procedure to obtain ellipsoidal approximations of the regions is also presented. • The results are illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis. • A novel Lyapunov-type stochastic predefined-time stable control algorithm is presented in Theorem 1. • Controller design based on the backstepping method is formulated through the power integrator technique. • The tan-type barrier Lyapunov function extends the order range and absorbs the inherent properties of the nonlinear terms. [ABSTRACT FROM AUTHOR]

The paper concentrates on the issue of distributed disturbance observer-based nonfragile bipartite consensus within nonlinear delayed multiagent systems, encompassing both leaderless and leader-following structures. The delays under consideration are nonuniform, manifesting in the state, the nonlinearity, and the communication processes. To suppress the external disturbances and the observer gain perturbations, distributed nonfragile disturbance observers pertaining to relative output and communication delays are developed to estimate the external disturbances for each agent. Employing the developed disturbance observer, distributed control protocols for nonfragile bipartite consensus are constructed incorporating states, estimated disturbances, and communication delays. These protocols can ensure bipartite consensus, compensate for external disturbances, and tolerate uncertainties in control gain. New augmented Lyapunov-Krasovskii functions are formulated by introducing the triple integral term and the augmented vector. The new bipartite consensus criteria for the studied multiagent systems are established with less conservatism by employing the techniques on second-order Bessel-Legendre integral inequality, reciprocally convex combination, and free weight matrix. Finally, numerical simulations and comparisons are performed for both leaderless and leader-following scenarios, thereby validating and enhancing the theoretical outcomes. • Multiagent systems with nonlinearity, disturbance and multiple delay, is considered. • Both cooperative and antagonistic relationships are all considered in consensus. • The perturbations in both observer and bipartite consensus protocol. • New Lyapunov-Krasovskii functions, and Bessel-Legendre inequality are employed. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic behavior of a tethered satellite system in an elliptical orbit as the tethered subsatellite is deployed from a mother satellite at an out-of-plane angle while maintaining the tether at a constant in-plane pitch angle by a predefined control force acting on the subsatellite. A variable-length pendulum model is employed to describe the purely out-of-plane tether deployment dynamics, from which an analytical tether deployment control law is derived. The stability condition of the analytical control law is examined by Floquet theory. The corresponding analytical deployment law is asymptotically stable, and the requirement for a positive tension control input is guaranteed to ensure the controllability of the tether system. Following deployment, the critical conditions for the out-of-plane libration of the tethered subsatellite to become chaotic during the station-keeping phase are examined. Finally, simulation results reveal that the proposed approach can effectively and rapidly identify periodic, quasiperiodic, and chaotic motions using bifurcation diagrams, which provides valuable insights for enhancing the stability and reliability of such tethered satellite systems. • Proposed an analytical deployment law for a purely out-of-plane tethered satellite. • Revealed nonlinear phenomena of the system during the station-keeping phase. • Explored bifurcation characteristic and chaotic windows of the system. [ABSTRACT FROM AUTHOR]

This paper studies the control problem for a continuous-time networked system with non-linearity in the state equation as well as in the input, as saturation. The system is considered under denial-of-service (DoS), attacks which cause the blockage of input and/or output components in the overall closed-loop model. An event-triggering scheme that is resilient in nature, along with an observer-based control, has been considered under DoS attacks. The resultant scheme ensures efficient network resources and excludes Zeno behavior naturally due to the presence of a minimum positive interevent delay. Then, an event-based switched non-linear model is presented to address both the event-triggering scheme and the presence of DoS blocking attacks. A piece-wise Lyapunov–Krasovskii functional method on the described non-linear model, resulting in the switched system, is considered for achieving an exponentially stable response by driving the required feasibility conditions. In the presence of a non-linear system with saturation in the actuator, the presented design establishes quantitative relationships among the exponential decay rate, active/sleeping intervals of attacks, parameters of the event-triggering condition, and sampling period of the system. After that, linear matrix inequalities are presented for designing an event-triggered controller with an observer, while the design also includes the region of convergence for dealing with the input non-linearity. Finally, comparative results for an offshore structure model with non-linearity in states as well as in actuator, are demonstrated to verify the results of the control scheme that is developed. It has been verified that our design is less conservative than the previous designs, and can handle the non-linearities in the dynamics of plant and actuator saturation more efficiently, while DoS attacks are also present. By applying our proposed method, the overshoot and undershoot are less than ±2.5 percent, while system states converge to the origin within 55 s. • An ϵ T-Lipschitz condition is used with a scaling factor ϵ and a variable matrix T • Non-linear control designed for system with input saturation and state non-linearity • Stability of the system is ensured in presence of DoS attacks with event triggering • Output feedback is utilized with switching non-linear observer having multiple gains • The joint design of all the required matrices using LK functions is utilized [ABSTRACT FROM AUTHOR]

This research presents a novel approach called 'Time-to-target-based multi-missile spatio-temporal cooperative guidance' This approach enables the simultaneous guidance of multiple missiles, allowing them to intercept a maneuvering target from different terminal intercept angles to maximize damage. The article introduces a finite-time optimal cooperative guidance technique to reduce the load on missile engines in the line-of-sight (LOS) direction. It proposes a time-varying sliding mode guidance scheme, which is parameterized by the remaining flight time, for both longitudinal and lateral LOS directions. The scheme helps prevent excessive initial acceleration in the longitudinal and lateral LOS directions while ensuring intercept angle constraints. The time-varying cooperative guidance law proposed in this study enables the simultaneous interception of a maneuvering target with different terminal intercept angles at the moment of terminal intercept. The numerical simulation results indicate that the multi-missile spatio-temporal cooperative guidance method is effective, superior, and robust. The method enables multiple missiles to achieve the minimum acceptable intercept distance at different terminal intercept angles while optimizing fuel in the LOS direction. • Enhanced 3D guidance : Synergizing a 3D line-of-sight coordinate system with nonlinear kinematics to expand interception areas and improve performance over linear methods. • Nonlinear finite-time temporal cooperative optimal guidance law : A novel nonlinear finite-time time cooperative optimal guidance method is proposed by combining finite-time optimal theory and multi-agent system optimal consensus theory. This temporal cooperative guidance method outperforms the existing methods in terms of fuel efficiency and accuracy, and alleviates the burden on the engine. • Advanced spatio cooperation guidance law with time-varying sliding mode approach: This paper presents a spatio cooperation guidance law utilizing a time-varying sliding mode approach. Unlike traditional space cooperation based on finite or fixed time theory, this innovative residual flight time-to-go based spatio cooperation method offers more accurate interception and superior angle tracking performance. It notably reduces the initial overload requirement and forms a spatio-temporal cooperation with temporal cooperation, ideally suited for simultaneously attacking maneuvering targets from different directions at the moment of terminal interception. This approach signifies a breakthrough in multi-dimensional target engagement efficiency. [ABSTRACT FROM AUTHOR]

This paper investigates a tracking control issue for a class of time-varying output constrained nonlinear systems subject to non-affine nonlinear faults and virtual control coefficients. In the controller design process, the nonlinear function is approximated by fuzzy logic systems. Utilizing a feasible function to convert the system, a new transformation strategy is proposed to handle the system with time-varying output constraints or without output constraints. The mean value theorem is applied to split non-affine faults, and the Nussbaum-type function is used to eliminate the effect of the unknown directional affine variable gain of input resulted from non-affine faults. Combined with adaptive fuzzy backstepping technology and the error transformation function, a new control strategy is presented, which not only deals with the time-varying output constraint but also handles non-affine faults, effectively. Finally, all closed-loop system signals are bounded, and the tracking error can converge to a small preset set. Two simulations are performed to confirm the validity of the presented strategy. • Nonlinear transformation functions are adapted to systems with or without output constraints. • Tracking error can converge to a small adjustable set and maintain within a prescribed range. • Updating estimates of virtual control coefficient online reduces system limitations. [ABSTRACT FROM AUTHOR]

The paper studies the control problem of an uncertain nonlinear system with tracking error constraint, unknown nonlinear functions and unknown control input gains. An asymmetric barrier Lyapunov function composed with predefined time prescribed performance function is constructed to ensure tracking error enters into the predefined asymmetric constraint in a given time. Then radial basis function neural network is adopted to approximate unknown functions. To reduce computation load, minimal-learning parameter technique is applied. Meanwhile, adaptive method is used to solve actuator faults and the unknown control input gains. Moreover, an adaptive neural control strategy is designed in the framework of backstepping method. An adaptive fixed time filter is developed for avoiding the "explosion of complexity" problem, where the convergence speed of the filter error is improved compared with fixed time filter. It is proved that all signals of the closed-loop system are bounded and tracking error is kept in its constraint boundary. At the end, compared numerical simulations and application simulation of a hypersonic vehicle are demonstrated to verify the efficiency of the designed control scheme. • A composed performance function is designed to ensure the tracking error enters into the constraint in a given time. • An adaptive fixed time filter is developed to solve the 'explosion of complexity' problem. • Based on minimal-learning parameter method, neural networks estimate unknown functions, which reduce computation load. • Compared simulation and application simulation of a hypersonic vehicle are given to test the efficiency of the controller. [ABSTRACT FROM AUTHOR]

In light of the expanding cyber-space applications, the imperative consideration of cyber-attack ramifications on system security is evident. This paper presents a resilient dynamic event-triggered fault detection scheme for a class of nonlinear interconnected systems subjected to denial of service (DoS) attacks. To counteract multifaceted threats, the co-design challenge involving switched-type fault detection filters and a resilient dynamic event-triggered transmission mechanism is addressed. In the design phase of the filters, the frequency information of the signal is considered comprehensively and linear solvable conditions ensuring desired augment system performance are delineated. Through a series of comparative simulation experiments, the findings support the conclusion that the proposed attack-tolerant fault detection mechanism not only conserves network resources but also demonstrates superior detection capabilities for specific frequency fault signals. • System vulnerability to multiple threats is considered. • Signal frequency information is utilized to enhance detection precision. • RDET strategy is co-designed with finite frequency fault detection filter. [ABSTRACT FROM AUTHOR]

In this paper, a novel event-triggered predictive iterative learning control (ET-PILC) method with random packet loss compensation (RPLC) mechanism is proposed for unknown nonlinear networked systems with random packet loss (RPL). First, a new RPLC mechanism is designed by utilizing both the historical and predictive data information to avoid the deterioration of control performance due to RPL. Then, a new event-triggered condition is designed based on the proposed RPLC mechanism to save communication resources and reduce computational burden. Moreover, the convergence of the modeling error and tracking control error are analyzed theoretically, and simulation results are given to demonstrate the effectiveness of the proposed method further. • A novel random packet loss compensation (RPLC) mechanism is designed by utilizing searched iterative historical data and predicted data. The proposed RPLC mechanism can avoid the use of old historical data and prevent invalid updates of control inputs. • A new event-triggered control (ETC) strategy is designed by utilizing the RPLC data, which can simultaneously incorporate historical, estimated and predicted system data into the designed event-triggered condition, to save communication resources and reduce computational burden. • Considering both RPLC and ETC strategy for the first time in the framework of PILC, we propose a novel ET-PILC with RPLC mechanism. It can not only compensate for missing data more effectively, but also guarantee the system performance and save resources. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive critic control method is designed to solve an optimal H ∞ tracking control problem for continuous nonlinear systems with nonzero equilibrium based on adaptive dynamic programming (ADP). To guarantee the finiteness of a cost function, traditional methods generally assume that the controlled system has a zero equilibrium point, which is not true in practical systems. In order to overcome such obstacle and realize H ∞ optimal tracking control, this paper proposes a novel cost function design with respect to disturbance, tracking error and the derivative of tracking error. Based on the designed cost function, the H ∞ control problem is formulated as two-player zero-sum differential games, and then a policy iteration (PI) algorithm is proposed to solve the corresponding Hamilton–Jacobi–Isaacs (HJI) equation. In order to obtain the online solution to the HJI equation, a single-critic neural network structure based on PI algorithm is established to learn the optimal control policy and the worst-case disturbance law. It is worth mentioning that the proposed adaptive critic control method can simplify the controller design process when the equilibrium of the systems is not zero. Finally, simulations are conducted to evaluate the tracking performance of the proposed control methods. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of designing distributed control law for a class nonlinear system in which the measurement outputs of the system are distributed in different subsystems. It leads to a challenge that the states of the original systems cannot be completely reconstructed by any single subsystem. In order to solve this problem, distributed state observers and the distributed observer-based distributed control problem emerges as the times require. However, the distributed observers problem of the nonlinear systems is rarely studied, and the distributed control law formed by distributed nonlinear observers has hardly ever been studied up to now. To this end, this paper develops the distributed high-gain observers for a class of nonlinear systems. Unlike the previous several results, our study has the ability to deal with model uncertainty, and devotes itself to overcoming the problem that the separation principle is not tenable. In addition, based on the state estimate generated by the designed distributed observer, an output feedback control law formed by applying the state estimate is developed. Furthermore, a class of sufficient conditions is proved for guaranteeing the error dynamics of the distributed observer and the state trajectory of the closed-loop system to enter an arbitrary small invariant set around the origin. Finally, the simulation results verify the effectiveness of the proposed method. • This paper proposed distributed-observer-based distributed control law for Lipschitz nonlinear systems with model mismatch. Both the error of distributed observer and the states of the closed-loop system can converge to the arbitrary invariant set. • Compared to the existing literature, this paper overcomes the coexistence of control input, nonlinearity, and uncertainty, while the existing works do not fix the control input into account. Besides, the existence of model mismatch is also deliberated. • This paper includes the observer feedback part based on the system output without relying on the assumptions used in the existing studies concerning distributed-estimation-based distributed control framework. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer. • A fixed-time distributed extended state observer (FxTDESO) containing a group of local observers is developed for an uncertain second-order nonlinear system. Each local observer can accurately reconstruct both the full state and lumped uncertainties in a fixed time. Compared to previous distributed extended state observers, the upper bound of the settling time of the observation errors is regardless of the initial conditions. • Unlike the existing fixed-time distributed observers which can only be used to estimate the system states and require the full state of the leader and full-state estimates from the observer nodes, both the states and uncertain dynamics can be reconstructed by our observer. Moreover, only output information of the leader and 1-dimensional output estimates of the local observer nodes are needed, which can effectively reduce the communication load. • When only the output information is available, it is challenging to find a way to analyze the fixed-time stability. To this end, a Lyapunov function is elaborated, and based on this, sufficient conditions for realizing fixed-time stability of the FxTDESO under time-invariant and time-varying disturbance are established, respectively. Furthermore, the FxTDESO design and stability analysis for a class of high-order nonlinear systems is briefly discussed. [ABSTRACT FROM AUTHOR]

Abrupt-motion tracking is challenging due to the target's unpredictable action. Although particle filter (PF) is suitable for target tracking of nonlinear non-Gaussian systems, it suffers from the problems of particle impoverishment and sample-size dependency. This paper proposed a quantum-inspired particle filter for abrupt-motion tracking. We apply the concept of quantum superposition to transform classical particles into quantum particles. Quantum representation and corresponding quantum operations are addressed to utilize quantum particles. The superposition property of quantum particles avoids the concerns of particle impoverishment and sample-size dependency. The proposed diversity-preserving quantum-enhanced particle filter (DQPF) obtains better accuracy and stability with fewer particles. A smaller sample size also helps to reduce computational complexity. Moreover, it has significant advantages for abrupt-motion tracking. The quantum particles are propagated at the prediction stage. They will exist at possible places when abrupt motion occurs, which reduces the tracking delay and enhances the tracking accuracy. This paper conducted experiments compared to state-of-the-art particle filter algorithms. The numerical results demonstrate that the DQPF is not susceptible to motion mode and particle number. Meanwhile, DQPF maintains excellent accuracy and stability. • We transformed classical particles into quantum ones. • We addressed quantum representation and corresponding quantum operations. • The proposed DQPF avoids particle impoverishment and sample-size dependency. • The proposed DQPF has significant advantages for abruptmotion tracking. [ABSTRACT FROM AUTHOR]

Frequent state monitoring and controller updates can enhance the precision of tracking control, while simultaneously overburdening the communication network transmission. In this paper, For the purpose of saving communication costs, we propose event-triggered control algorithms for the optimal tracking control problem. First, we reconstruct the discrete-time nonlinear system into a converted system. Then, the adaptive dynamic programming algorithm is employed to find the optimal controller off-line, and the event-triggered scheme is used to reduce the communication costs online. Novel triggering conditions with fewer assumptions are designed to implement the event-triggered scheme. Different from existing works, the event-triggered scheme can be introduced not only into the converted system but also into the actual system, which is more practical because the actual controller is what one can only access in practice. In addition, with the developed algorithms, the tracking error can be proved to be stable at the origin, in other words, the actual system can be guaranteed to track the desired trajectory. Algorithms developed in this paper are implemented by three neural networks, the model network, the action network and the critic network. Finally, examples are presented to verify the effectiveness and rationality of the algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the efficient methods for option pricing under multivariate rough volatility models. The characteristic functions of the asset log-price, which play important role in the option pricing under the multivariate rough volatility models, are determined by a system of parametric nonlinear fractional Riccati equations. This paper obtains the results on the existence, uniqueness and regularity of the solutions to the parametric nonlinear fractional Riccati equations, proposes a high-order scheme to solve the system and proves the high-order convergence. The option pricing problem is solved by the Fourier-cosine formula with the fast approximation of the characteristic functions. Numerical examples are carried out to confirm the theoretical results and show efficiency of the methods. [ABSTRACT FROM AUTHOR]

• This paper provides a FDEFLN-based nonlinear filtering scheme and its filtered-s version in a computationally efficient manner. • The stability, steady-state performance and computational complexity of the proposed frequency domain algorithms are derived and analyzed. • With applications to NSI, NAEC and NANC, the notable computational advantages of the proposed FDEFLN-based algorithms have been verified. The exponential functional link network (EFLN) filter has attracted tremendous interest due to its enhanced nonlinear modeling capability. However, the computational complexity will dramatically increase with the dimension growth of the EFLN-based filter. To improve the computational efficiency, we propose a novel frequency domain exponential functional link network (FDEFLN) filter in this paper. The idea is to organize the samples in blocks of expanded input data, transform them from time domain to frequency domain, and thus execute the filtering and adaptation procedures in frequency domain with the overlap-save method. A FDEFLN-based nonlinear active noise control (NANC) system has also been developed to form the frequency domain exponential filtered-s least mean-square (FDEFsLMS) algorithm. Moreover, the stability, steady-state performance and computational complexity of algorithms are analyzed. Finally, several numerical experiments corroborate the proposed FDEFLN-based algorithms in nonlinear system identification, acoustic echo cancellation and NANC implementations, which demonstrate much better computational efficiency. [ABSTRACT FROM AUTHOR]

Intermittent control stands as a valuable strategy for resource conservation and cost reduction across diverse systems. Nonetheless, prevailing research is intractable to address the challenges posed by robust optimal intermittent control of nonlinear input-affine systems with unmatched uncertainties. This paper aims to fill this gap. Initially, we introduce an enhanced finite-time intermittent control approach to ensure stability within nonlinear dynamic systems harboring bounded errors. A neural networks (NNs) state observer is constructed to estimate system information. Subsequently, an optimal intermittent controller that operates within a finite time span, guaranteeing system stability by employing the Hamilton–Jacobi–Bellman (HJB) methodology. Furthermore, we devise an output information-based event-triggered intermittent (ETI) approach rooted in the robust adaptive dynamic programming (ADP) algorithm, furnishing an optimal intermittent control law. In this process, a critic NNs is introduced to estimate the cost function and optimal intermittent controller. Simulation results show that our proposed method is superior to existing intermittent control strategies. • We study the robust intermittent affine control system with unmatched uncertainties. • In contrast to the existing ET ADP, we introduce a novel intermittent ET ADP. • The proposed optimal output intermittent control show better control performance. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits. • A decentralized prescribed-time (PT) tracking problem is addressed using quantized output feedback (QOF). • A decentralized memoryless PT state observer based on quantized local outputs is developed. • The practical PT stability of the proposed QOF control system is analyzed mathematically. [ABSTRACT FROM AUTHOR]

The paper discusses investigating the behavior of the discrete nonlinear Schrödinger (DNLS) system. This technique combines the exponential function method and the rational function method to obtain exact solutions for a wide range of nonlinear differential-difference equations (NDDEs). The objective is to utilize the generalized exponential rational function (GERF) technique to analyze and understand the dynamics of the DNLS system. Overall, this research contributes to advancing our knowledge of nonlinear dynamics in optical fibers and establishes a solid foundation for further exploration of soliton applications. • We focused on investigating discrete soliton solutions in a system that describes the propagation. • The investigation of these soliton solutions opens up new avenues for applications in optical communications. • We discovered various families of soliton solutions. [ABSTRACT FROM AUTHOR]

It is the first report about fault-tolerant-based prescribed performance control of switched nonlinear systems under multiple faults. The concerned faults include not only external faults but also actuator faults. In the process of backstepping control design, prescribed performance control is fully considered, and the combination of unknown nonlinear functions is estimated by multi-dimensional Taylor network. Finally, the developed adaptive fault-tolerant control strategy guarantees the boundedness of all controlled signals while prescribed tracking performance is satisfied. In an effort to further manifest the validity of the fault-tolerant controller, a numerical simulation and a practical simulation are introduced. • This paper is dedicated to balancing prescribed tracking performance and multiple faults. • It is the first time that actuator fault, external fault are discussed in the complicated switching framework. • The adaptive fault-tolerant MTN-based controller is developed to cope with performance constraints. [ABSTRACT FROM AUTHOR]

In this paper, balance control of a bicycle robot is studied without either a trail or a mechanical regulator when the robot moves in an approximately rectilinear motion. Based on the principle of moment balance, an input nonaffine nonlinear dynamics model of the bicycle robot is established. A driving velocity condition is proposed to maintain the robot balance. The nonaffine nonlinear system is transformed into an affine nonlinear system by defining the equivalent control. Subsequently, a feedback linearization controller is designed for the equivalent control. We design a combined control algorithm of synchronous policy iteration based on the actor–critic architecture. The actor neural network (NN) is designed based on the feedback linearization control law. Weight tuning laws for the critic and actor NNs are proposed. The system closed-loop stability and convergence of the NN weights are guaranteed based on the Lyapunov analysis. The optimality of the equivalent control policy is guaranteed. To satisfy the driving velocity condition, the values of the steering angle and driving velocity are determined based on the optimal equivalent control. The effectiveness of the proposed algorithm is verified through simulations and real experiments. • A nonaffine nonlinear system of a bicycle robot is presented. • We set the driving velocity first and then determine the steering angle. • The actor neural network is designed using the model-based control law. [ABSTRACT FROM AUTHOR]

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis. • Both the system delay and the distributed delay is considered in MASs; • An innovative distributed impulsive controller is designed, which increases the control flexibility and accelerates the speed of consensus; • The leader-following consensus is realized based on two different functions of impulsive effects. [ABSTRACT FROM AUTHOR]

This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction–diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H ∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H ∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh–Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology. • This paper addresses the problem of practical consensus with spatiotemporal dynamics. • The multi-agent system is modeled by a nonlinear reaction–diffusion equation. • An H ∞ boundary consensus control is proposed to suppress the external disturbances. • The controller needs a fewer actuators than ones distributed inner spatial domain. • The controller gives a tradeoff between optimal performances and actuator saturation. [ABSTRACT FROM AUTHOR]

• This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. • It is shown that the size of delay in continuous dynamics can be smaller or bigger than the impulsive intervals. • It removes the restriction on the magnitude relationship between the delay in continuous flow and the impulsive delay. • The rate coefficients are flexible and the impulsive delay can be integrated to guarantee the stabilization of impulses. • The synchronization of chaotic neural network is formalized in terms of linear matrix inequalities. This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. Some sufficient conditions are provided for establishing stability property in terms of exponential Lyapunov-Razumikhin functions. It is shown that the size of delay in continuous dynamics can be flexible. Specially, it can be smaller or larger than the impulsive intervals, and there is no magnitude relationship between the delay in continuous flow and impulsive delay. In most existing results, from the impulsive control point of view, the Lyapunov functions were based on the assumption that there was a common threshold at every impulse point. In this study, utilizing the proposed method of average impulsive estimation (AIE), the rate coefficients are flexible, and the impulsive delay can be integrated to guarantee the effect of stabilization of impulses. As an application, the theoretical results are applied to the synchronization of a chaotic neural network, and the impulsive control input is formalized in terms of linear matrix inequalities (LMIs). The efficiency of the derived results is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

The drift-diffusion equations are a class of nonlinear systems in the application of semiconductor devices. High efficient solution methods for solving these equations play a significant role in numerical simulations. Some nonlinear iterative methods, including Newton method and Gummel method, are usually used to solve the discretized drift-diffusion equations. Therefore, a nonlinear initial iterate should be given. The nonlinear initial iterate has a strong influence on the solution method. Typically, the related physical values in the equilibrium state, including the potential, the electron concentration, and the hole concentration, are used as the initial iterate for solving the equations with a given bias voltage. Due to the strong nonlinearity, by using the typical initial iterate, the nonlinear iterate converges slowly or even can not converge when the given bias voltage is large. In this paper, an efficient initial iterate is constructed by exploiting the application features of the drift-diffusion equations. The key idea is to construct an approximate equation of the drift-diffusion equations by neglecting the recombination effect and casting the effects of the bias voltage on carriers' quasi-Fermi potential. And the initial iterate is obtained by solving the approximate equation. Some physical interpretations and theoretical analyses for the proposed method are given. Numerical results show that the proposed initial iterate is effective, and the number of nonlinear iterations can be reduced by about 90% at most compared to the typical initial iterate. In some cases, the nonlinear iteration can not converge when the typical initial iterate is used, while the iteration converges if the new initial iterate in this paper is used. [ABSTRACT FROM AUTHOR]

• This paper aims to construct a NN DETAC scheme for interconnected nonlinear system against Dos attacks and external disturbances. • A switching-type adaptive state observer with a disturbance estimation value is proposed and an anti-disturbance decentralized event-triggered adaptive control scheme is developed. The proposed method can enhance system anti-disturbance ability. • Different from the sampled-data control scheme in the related literature, the NN DETAC scheme is developed, which can efficiently save communication resources. • By employing the properties of the hyperbolic tangent function, the interconnection terms no longer meet the global Lipschitz conditions, which relaxes the constrain condition. This paper discusses the issue of decentralized event-triggered adaptive neural network (NN) control for nonstrict-feedback nonlinear interconnected systems with external disturbances and intermittent denial-of-service (DoS) attacks. In the presence of DoS attack, all state variables are not used to design a feedback controller via the standard backstepping method. To solve this problem, a novel switching-type adaptive state observer with a disturbance compensation is constructed, where the disturbance compensation is obtained via constructing a disturbance observer. A decentralized event-triggered adaptive controller is designed by using the backstepping method to weaken the influences of DoS attack and the waste of communication resources, where a first-order sliding mode differentiator is introduced to prevent the "calculation explosion". By using linear matrix inequality techniques, some solvable sufficient conditions are attained to derive the observer gain. The closed-loop system is proved to be stable via the improved average dell time method and the piecewise Lyapunov stability theories. This control scheme ensures that all closed-loop signals remain bounded. Finally, simulation results are utilized to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a new control strategy to deal with three different types of uncertainties for a class of time-varying delay nonlinear systems. Quite different from related celebrated works, the considered systems allow the existence of parameter uncertainties in the output function and nonlinearities, dynamic uncertainties of the unmeasurable state, and continuous external disturbances, which invokes the motivation of the paper. The objective is to construct a continuous output feedback controller by utilizing a new restructured integral function and the double-domination method. The novelty control design is the capability of tackling zero-dynamic and unknown output function simultaneously, thereby guaranteeing the state convergence of the closed-loop system. Finally, the proposed scheme is applied to a practical example and a numerical one simultaneously to demonstrate the effectiveness and the superiority. • This paper is an important theoretical work to deal with the output feedback stabilization problem of time-delay nonlinear systems, since it provides a new idea to handle parameter uncertainties in the output function and nonlinearities, dynamic uncertainties of the unmeasurable state, and continuous external disturbances. • This method overcomes the influence of dynamic/parametric uncertainties and time-varying terms, and provides an insight for the combination of output feedback stabilizer and state observer for uncertain control systems. • To eliminate the effect of dynamic uncertainties, a nondecreasing positive continuous function is used to construct an appropriate integral Lyapunov function in stability analysis. [ABSTRACT FROM AUTHOR]

[Display omitted] • A noval event-triggered control strategy is developed by integrating backstepping method and emulation method into the event-triggered control study the distributed tracking of nonlinear MASs. Compared with the single-agent system, the control design in this paper is more complicated since that its's necessary to consider information interaction between each agent. • The event-triggered control strategy saves more communication and computing resources compared with the periodic sampled-data control schemes. In addition, The introduction of event-triggering mechanism, on the one hand, leads to complex discontinuity of the system, which renders the analysis and synthesis of the MASs more difficult than MASs with continuous controllers. • The dynamic of the i th follower discussed in this paper contains N i integrators and nonlinearities, which is more general and more complex than linear MASs, and first-order and second-order MASs. The existence of nonlinear functions makes the design and construction process of event-triggered controller more complicated. This paper investigates the problem of distributed output tracking for nonlinear multi-agent systems via event-triggered control under a directed graph topology inspired by the advantage that event-triggered control can effectively save resources and the wide application of multi-agent systems. By backstepping and emulation method, the event-triggered control strategy is put forward, by which a series of event-triggered controllers and event-triggering mechanisms with absolute or relative threshold are designed. An inevitable problem on event-triggered control, called Zeno phenomenon, is avoided by guaranteeing a positive minimum inter-execution interval. We can see from the event-triggered control strategy that the closed-loop system has a unique solution and tracking error could be adjusted to arbitrarily small while ensuring the boundedness of all states. Finally, a numerical example is shown to verify the validity of the conclusion. [ABSTRACT FROM AUTHOR]

• This paper studies the finite-time stabilization of nonlinear systems with impulsive disturbance via saturated control. • A potential relationship between saturation structure and impulsive disturbance is presented for finite-time stabilization. • The estimations of the domain of attraction and the settling-time are derived. This paper studies the finite-time stabilization (FTS) of nonlinear systems with impulsive disturbance, where the effect of saturation structure on the control input is fully considered. By establishing a potential relationship between saturation structure and impulsive disturbance, some FTS criteria are presented via a class of saturated control input, where estimations of domain of attraction and settling-time are derived. Compared with the control input without saturation structure, the constraints on impulse time sequence are strengthened to guarantee that the saturated control input has an effective stabilizing effect on the system. Based on such constraints, the system subjected to impulsive disturbance can still achieve FTS. Then theoretical results are applied to finite-time synchronization for a class of impulsive dynamical networks. Finally, two examples and their simulations are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The newly developed generalized scalar auxiliary variable (GSAV) approaches are very popular methods that can be applied to construct high-accuracy energy-preserving schemes for conservative systems. However, these proposed high-order schemes are fully-implicit and have the disadvantages of huge calculating quantities and long computing time for solving nonlinear systems. Therefore, we develop in this paper explicit energy-preserving schemes to deal with the coupled nonlinear Schrödinger equation by combining the Lie-group method and GSAV approaches. The given schemes are very efficient, have high accuracy, and can inherit the modified energy of the system. Ample numerical results are presented to confirm the developed schemes' efficiency, accuracy, and conservation. [ABSTRACT FROM AUTHOR]

In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in C ([ 0 , T ] ; L 2 (T 3)) for any initial data in H β ¯ (T 3) (β ¯ > 0), by exhibiting that the total energy and the cross helicity can be controlled in a given positive time interval. Our results extend the non-uniqueness results of the ideal MHD system to the viscous and resistive MHD system. Different from the ideal MHD system, the dissipative effect in the viscous and resistive MHD system prevents the nonlinear term from balancing the stress error ( R ˚ q , M ˚ q) as doing in [4]. We introduce the box flows and construct the perturbation consisting in seven different kinds of flows in convex integral scheme, which ensures that the iteration works and yields the non-uniqueness. [ABSTRACT FROM AUTHOR]

Existing diffusion models can only do tasks for either restoration or binarization of degraded document images; in this paper, we pay close attention to the problem of simultaneous restoration and binarization. We first introduce a model of image formation for degraded document images, which decomposes a degraded document image into the product of background and foreground components. Then a weakly coupled nonlinear diffusion system is developed for simultaneous restoration and binarization of degraded document images. In this diffusion system, the first equation is used to estimate background component and the second equation is responsible for the foreground component. The restored and binarized images are finally obtained by the estimated background and foreground components, respectively. Two coupled diffusion equations are solved alternately by explicit finite differencing. The proposed model is tested on some degraded document images that represent five types of typical degradations including bleed-through, complex background, page stains, stamps and smeared ink, and is compared with eight closely related models for degraded document binarization, qualitatively and quantitatively. Experimental results illustrate that the proposed model has shown promising results in terms of restoration and binarization of degrade document images. • Model of image formation is introduced for describing degraded document images. • Nonlinear diffusion system is proposed for restoration and binarization of degraded text images. • Our model has shown promising results in terms of simultaneous restoration and binarization. [ABSTRACT FROM AUTHOR]

The Pigeon-Inspired optimization (PIO) algorithm is a novel intelligent optimization algorithm inspired by birds' behavior as their travel. This; behavior modeled to be used for solving many optimization problems in different fields. However; it always suffers from unstable behavior when used with nonlinear; time-varying systems. In; this paper, this algorithm is adapted to calculate the optimum controller gains for roll and pitch channels in a guided tactical missile. The; vehicle model is presented in a nonlinear; form and then shown in a linearized form for the sake of an autopilot design. The PIO; algorithm is supported and accompanied by an adaptive algorithm to determine the initial states and constraints for the PIO algorithm to enhance the behavior of the optimization algorithm to speed up the convergence rate to reach an optimum and feasible solution. Also; an estimation function is incorporated to estimate model parameters variation such as dynamic pressure, stability derivatives, and mass properties. Meanwhile; a comparative analysis is carried out with original PIO and particle swarm optimization algorithms, utilizing a non-linear; model with the presence of noise source and disturbance to ensure the ability of the algorithm to make the autopilot robust and stable against several sources of uncertainties. [ABSTRACT FROM AUTHOR]

This paper concerns the tracking control problem of a class of uncertain nonlinear systems subject to deferred time-varying state constraints and external disturbances. The states of the system are free in the initial phase and are restricted by some time-varying constraints after a particular time. A class of novel shifting functions are defined, which make any initial states that beyond the constraint region move to the desired position (such as zero). Thereafter, a new state transformation is implemented for the shifted state, which transforms the state constraint problem into the boundedness of a new variable. Compared with the existing BLF method, this approach avoids feasibility test for virtual control variables. Adaptive backstepping control and dynamic surface control are used in system controller design and stability analysis, and the ideal tracking performance is achieved. Finally, simulation example and comparative studies are carried out to illustrate the effectiveness and outstanding characteristics of the proposed approach. Simulation results show that the proposed control scheme broadens the scope of application, shortens running time and improves control efficiency compared with the existing control strategies. • A class of lower-degree shifting function are defined. • A novel state transformation is constructed. • The proposed control scheme broadens the application scope and improves the control efficiency. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant prescribed performance control problem for a class of multiple-input single-output unknown nonlinear systems subject to process faults and actuator failures. In contrast to the related works, we consider a general class of nonlinear systems with both multiplicative nonlinearities and additive nonlinearities corrupted by the process faults; only the boundedness of the process faults and the continuity of the nonlinear functions are required, without the explicit or fixed structures of the fault functions. To conquer this problem, a less-demanding and low-complexity fault-tolerant prescribed performance control approach is proposed. The controller is independent of the specific information of faults or the system model and does not invoke fault diagnosis or neural/fuzzy approximation to acquire such knowledge. It achieves the reference tracking with the predefined rate and accuracy. A comparative simulation on a single-link robot is conducted to illustrate the effectiveness and superiority of the proposed approach. • Both process faults and actuator failures are considered. • The virtual control coefficients are time-varying nonlinear functions. • We consider a general class of systems with multiplicative and additive nonlinearities. • Both multiplicative and additive nonlinearities are impacted by process faults. • The reference tracking with predefined rate and accuracy is achieved. [ABSTRACT FROM AUTHOR]