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In this paper, a temporal second order two-grid difference scheme is proposed for the two-dimensional nonlinear time-fractional partial integro-differential equations with a weakly singular kernel. The first-order backward difference and L 1 formula are used in the temporal direction to estimate the first level of time, the L 2 − 1 σ formula and L 1 -type formula are used in the temporal direction for later time steps, and the central difference formula is used in the spatial directions. To improve the computational efficiency of nonlinear system, an efficient time two-grid algorithm is proposed. This algorithm firstly solves a nonlinear system on the coarse grid, and then the Lagrangian linear interpolation is applied on the coarse grid to estimate the function values on the fine grid. The stability and convergence of the two-grid difference scheme are analyzed by the energy method. The convergence order of the two-grid difference scheme is O (τ F 2 + τ C 4 + h x 2 + h y 2) , where τ F and τ C are the time step sizes of fine grid and coarse grid respectively, while h x and h y are the space step sizes. Numerical experiments show that the accuracy of the theoretical analysis and the efficiency of the two-grid algorithm. [ABSTRACT FROM AUTHOR]

Resonance and bifurcation are prominent and significant features observed in various nonlinear systems, often leading to catastrophic failure in practical engineering. This paper investigates, under an analytical and numerical perspective, the dynamical characteristics of a fractional Rayleigh oscillator with distributed time delay. Firstly, through the application of the multiple scales method, we derive approximated analytical solutions and amplitude–frequency equations for the regions near both primary and secondary resonances. The stability conditions of steady-state motions and the existence region of the subharmonic response are also obtained. Furthermore, to validate the accuracy of the approximated solutions, the results are compared with numerical solutions derived from the Caputo scheme, revealing a high concordance between them. Then, a comprehensive study on response curves is conducted for the system under different nonlinear damping, fractional parameters and delay strength. Finally, we identify and discuss the presence of the forked bifurcation within the system. [ABSTRACT FROM AUTHOR]

This paper considers a quantized consensus problem for nonlinear multi-agent systems (MAS) using iterative learning control (ILC). For actual digital communication networks, agents can only transmit state information with limited bandwidth. Therefore, a Sigma-Delta (Σ Δ) quantizer with a finite number of quantized bits is used to satisfy the communication network requirements. In addition, the introduction of network issues like input saturation and time delay make the problem more practically relevant. Due to the discontinuity caused by quantization, Filippov's non-smooth analysis theory is required to analyze the convergence performance of the MAS. The desired asymptotic consensus can be achieved with limited quantized information and possibly even a single bit between each pair of adjacent agents. Finally, numerical simulations are presented to illustrate the effectiveness of our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the fixed-time control for a class of second-order nonlinear systems with matched disturbance is addressed by using terminal sliding mode control technique. To improve the control performance of traditional fixed-time control method, a new fixed-time stability theorem is constructed by introducing a simple linear term, and theoretical analysis shows that the proposed control method provides faster convergence speed and more accurate estimate of the upper bound of settling time. Moreover, the practical fixed-time stability is also discussed in details. Based on the proposed fixed-time stability theorem, a fixed-time terminal sliding mode controller for a class of second-order nonlinear system is designed to obtain a bounded settling time independently of the initial conditions of the system. Simulations are carried out to verify the feasibility of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem for nonlinear multiagent systems (MASs) with unknown time-varying measurement sensitivity and infinite communication delays. Unlike existing works, the output measurement sensitivity is described as time-varying, and an infinite communication delay is considered between the agents. Under this condition, a novel output feedback control algorithm is developed. First, based on the hierarchical technique and Lyapunov-based time-domain method, the high-gain compensator and observer are constructed to tolerate the effect of infinite communication delays and accurately estimate the state of the leader. Subsequently, a new distributed k-filter and output feedback controller are proposed, which not only further relax the traditional Lipschitz conditional conservatism but also greatly simplify the design process. It is proved that the closed-loop system is globally stable and all agents can achieve consensus. Finally, the effectiveness of the proposed method is verified through the simulation of the single-link manipulators. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal backstepping control strategy for strict-feedback nonlinear systems subject to input saturation and time-varying partial output constraints. Compared with the existing results on output constraints, the time-varying partial output constraint is a more general constraint that can start and end at any time during the system operation, or remain unconstrained, which can be called as output constraints occurring in a limited time interval (OCOLT). A special barrier function is embedded into the optimal performance index function to satisfy the OCOLT condition under the optimal control framework, and a shift function is introduced to address the function discontinuity caused by the OCOLT problem. Then, an auxiliary system and a disturbance observer are respectively constructed to handle the influence of the input saturation and compounded disturbances. Meanwhile, the simplified reinforcement learning algorithm, employing the identifier-critic-actor architecture, is developed to achieve the optimal control objective within the framework of the backstepping technology. Moreover, the proposed optimal control method ensures the semi-globally uniformly ultimately bounded of all signals within the closed-loop system. Finally, two simulation examples are given to further prove the effectiveness of the presented optimal control approach. [ABSTRACT FROM AUTHOR]

The control input derived from model predictive control (MPC) scheme depends on the receding horizon whose length needs to be determined. Design length is also a trade-off between computational complexity and optimization metrics. To this end, a framework for adaptive selection of the horizon length has been developed for discrete systems in previous works. In this paper, this framework is extended to continuous nonlinear systems. A new algorithm is presented to solve the problem of how to adaptively select the horizon length. Then, according to the traditional method and the robust MPC scheme based on tubes, the recursive feasibility and robustness of the algorithm (the adaptive horizon nonlinear model predictive control, called AH-NMPC) for quasi-infinite time domain adaptive horizontal continuous-time nonlinear systems are proved. Finally, the NMPC controller is used to perform path-tracking experiments on an autonomous vehicle to verify the good effects of the algorithm (AH-NMPC). [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of asymptotic tracking control for a class of interconnected p -normal nonlinear systems (p -NNS) with full-state constraints (FSCs). An event-triggered mechanism is constructed by introducing a new dynamic variable. It effectively reduces the update frequency of the controller compared to temporal-triggered. By building a new barrier function, the unknown functions of the system are converted into unknown scalars, which will be disposed of by the adaptive technique. To implement the FSCs control, we propose a low-complexity constrained control scheme while removing the condition that the initial value of the output is constrained. According to Barbalat's lemma, it is proved that the output signal can asymptotically track the predetermined signal, and the system states are kept within the constraint bound, with all signals bounded. Finally, two simulation examples illustrate the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of power efficiency evaluation for n -ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class. • Power efficiency modeling and efficiency maps computation for physical systems. • Interchangeable efficiency maps computed on the different systems energetic ports. • Highlighting of intrinsic properties and of a design parameter for two-ports systems. • Efficiency maps computation and intrinsic characteristics of planetary gear sets. [ABSTRACT FROM AUTHOR]

Different from the majority of existing results that focus on the passivity analysis of nonlinear systems, this paper attempts to analyze the more general QSR-dissipativity of fractional-order neural networks that own output coupling and multiple coupled weights, where outer coupling weights can be adjusted online by developing an adaptation law. Using the linear matrix inequality technique, several sufficient criteria that not only guarantee the QSR-dissipativity of the network system but also achieve global synchronization even under zero input are established. Of particular significance is the proposal of a fractional Lyapunov-like lemma, which plays a crucial role in verifying the asymptotic stability of synchronization errors. Finally, a simulation example is presented to verify the plausibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method. [ABSTRACT FROM AUTHOR]

In this paper, the l 2 − l ∞ state estimation problem of discrete-time nonlinear systems (DTNSs) with time-varying delay is studied. The main objective of this paper is to design a state estimator that guarantees not only the global h -stability of the error system in the absence of interference, but also that the output peak value of the error system remains within a certain range under the zero initial conditions. A direct analysis method based on the system solutions is presented, which gives a sufficient condition to decide whether the designed state estimator satisfies the expectation. The method does not follow the construct of any Lyapunov–Krasovskii functional (LKF), thus greatly reducing the workload and complexity of calculation. Finally, three simulation examples are presented to illustrate the applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we investigate a system of coupled inequalities consisting of a variational–hemivariational inequality and a quasi-hemivariational inequality on Banach spaces. The approach is topological, and a wide variety of existence results is established for both bounded and unbounded constraint sets in real reflexive Banach spaces. Applications to Contact Mechanics are provided in the last section of the paper. More precisely, we consider a contact model with (possibly) multivalued constitutive law whose variational formulation leads to a coupled system of inequalities. The weak solvability of the problem is proved via employing the theoretical results obtained in the previous section. The novelty of our approach comes from the fact that we consider two potential contact zones and the variational formulation allows us to determine simultaneously the displacement field and the Cauchy stress tensor. • A system of coupled inequalities is introduced and studied. • The weak solvability of the system of coupled inequalities is proved. • A contact model involving multivalued and nonmonotone constitutive laws is explored. [ABSTRACT FROM AUTHOR]

This paper considers a data-driven method to detect stealthy replay attacks on cyber-physical systems (CPSs) whose models are unknown. Most existing attack detection methods assume the system dynamic is known. However, due to the large scale and complexity of the system, it is difficult to get an accurate model of a CPS. This paper uses a moving window subspace identification method to construct a linear discrete time-varying model of CPS. The controllability and observability of the obtained model are proved. On this basis, the replay attack is transformed into a detectable additive attack using the output coding strategy. Then, considering modeling errors, a time-varying H ∞ filter is designed, and a detection function based on the output residual is constructed. When the system works without any attacks, the detection function approaches a limited threshold. On the contrary, that function will increase extremely larger than the threshold when the replay attack occurs. The detectability of our scheme for attacks is also mathematically proven. Finally, to verify the effectiveness of the proposed scheme, we provide simulation results on a linear motor system and a nonlinear robotic system. [ABSTRACT FROM AUTHOR]

In this paper, an approximating state-dependent control (ASC) method with modified pattern search (MPS) optimization for nonlinear optimal control problem is proposed. First, by converting the nonlinear optimal control problem into a number of interrelated time-varying linear quadratic regulator subproblems, the ASC method can solve each subproblem iteratively until the approximate solution is obtained. Second, in each iterative control process, the MPS is used to solve the controllability optimization problem. The optimal state-dependent weighting coefficients are obtained during the MPS optimization. Moreover, the MPS uses simplex gradient to design the search direction, which makes the optimization process efficient and fast. The convergence of MPS optimization is also proved in this paper. Finally, two simulation examples are given to illustrate the effectiveness of ASC method using the MPS optimization. The result shows that the ASC method can reduce the iterations of the approximate solution, and the MPS optimization can optimize the control performance of the ASC method. • State-dependent control method for nonlinear system. • Optimization of control parameters by modified pattern search. • Design of approximating solving process. [ABSTRACT FROM AUTHOR]

For uncertain fractional-order nonlinear systems (UFONS) with unknown control coefficients and intermittent actuator faults, the asymptotic tracking control problem is investigated in this paper. Firstly, to weaken the influence of virtual control coefficients and intermittent actuator faults, a smooth fractional-order projection operator-based adaptive compensation mechanism is presented. Additionally, a fractional-order nonlinear filter is constructed to replace the fractional-order derivative of virtual control functions approximately, which not only avoids the issue of complexity explosion existed in backstepping control frame, but fully compensates the effects of boundary errors caused by the employed filter in spite of the unknown virtual control coefficient. By constructing a fractional Lyapunov function from the property of projection operator, it is proved that all signals in the closed-loop system are bounded, and the asymptotic tracking control object is achieved. Definitively, a simulation study is presented to verify the availability of the presented method. • This paper investigates the issue of asymptotic tracking control design for fractional-order nonlinear systems with unknown control coefficients and actuator faults. • Firstly, in order to weaken the influence of virtual control coefficient, an adaptive compensation mechanism based on the smooth fractional-order projection operator design method is proposed. • Additionally, a fractional-order nonlinear filter is constructed to approximately replace the virtual control functions as well as its fractional-order derivative, which not only avoids the inherent complexity explosion problem under the framework of backstepping, but also fully compensates the effect of boundary error caused by the introduced filter when the virtual control coefficient is unknown. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive event-triggered (AET) control, efficient model predictive control (EMPC) and output feedback control co-design approach for uncertain nonlinear systems over networks with bounded disturbance and data loss. The AET control involving a novel adaptive law is utilized to further reduce data transmission in networked control systems. Involving the technique of quadratic boundedness (QB), a class of output feedback predictive controllers based on the EMPC strategy are designed by minimizing several offline optimization problems and one online optimization problem. The approach in this paper, which transfers abundant online design work to offline, provides an offline determined augmented control invariant set for significantly reducing real-time computational load. Through the introduction of a novel matrix partition method moreover, the conventional online optimization problem of EMPC is transformed into a new form which is convenient to solve in this paper. A numerical example including some comparative experiments is proposed to clarify the availability of this approach. [ABSTRACT FROM AUTHOR]

In this paper, the containment control problem is investigated for a class of non-strict feedback nonlinear multi-agent systems with arbitrary initial states. The state observation disturbance, defined as the deviation between the observed and true values of the state, is taken into account in the addressed system. Fuzzy logic systems and adaptive techniques are accordingly introduced to handle the unknown nonlinear terms and unknown disturbances. Based on a transformation function and a new Lyapunov function, an improved fuzzy adaptive control protocol is developed, which ensures that the output tracking error of each follower converges to a predefined region within a predefined settling time and allows the initial states of the agents to be arbitrarily bounded. Moreover, the error (between the input and output of the filter inherent to the dynamic surface control) can be accurately compensated under the newly designed Lyapunov function. The simultaneous consideration of the asymmetric input saturation and unknown time-varying control gain coefficients in the model makes the results established in this paper more general. Finally, the effectiveness of the proposed control protocol is verified by two simulation experiments. • Agent's system is the more general non-strict feedback system. • The initial value of the agent's state can be arbitrary. • State observation disturbance is considered. • This paper employs adaptive control techniques. [ABSTRACT FROM AUTHOR]

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, a second-order-disturbance-observer-based distributed consensus control scheme is designed for a class of nonlinear multi-agent systems with input constraints. The second-order disturbance observer tracks the disturbance better than the common first-order disturbance observer. This paper provides the analysis of two kinds of disturbance observers and then compares the results from a simulation of the two types of observers. In the controller design process, a hyperbolic tangent function is used to limit output feedback in the control law. The overall closed-loop system reaches global stability with disturbance and the tracking errors exponentially converge without disturbance. The effectiveness of the proposed control law is illustrated by simulation results. • A novel disturbance observer is proposed. The estimation error is smaller. • The overall stability of the systems and the input constraints are realized. • Multi-agent systems converge exponentially with input constraints. [ABSTRACT FROM AUTHOR]

Due to the maturation of research on chaos and secure communication, the control technology of nonlinear systems, specifically chaos synchronization, has captured the attention of numerous researchers. Focusing on the issues of inflexibility in the design of chaotic synchronization controllers, the need for prior synchronization of the target system structure, and noise's disruptive impact on synchronization, this paper presents solutions that enhance the practical application of chaos. Firstly, the RBF neural controller is adjusted in this paper to bolster the control precision of the chaotic system and enhance its resilience to external disturbances. Secondly, this article presents an enhanced PSO optimization algorithm for the improved RBF neural controller to improve the optimization efficiency of the controller parameters. Finally, the simulation results of the Lorenz system validate the feasibility of the proposed synchronization control scheme. Additionally, the use of chaotic synchronization in image encryption demonstrates that synchronization accuracy can fulfill the requirements of image encryption application scenarios. • The structure of the RBF neural controller is improved to achieve better synchronization control performance, including synchronization accuracy and noise resistance. • The PSO algorithm is improved specifically for the intelligent chaotic controller studied in this article to enhance the efficiency of searching for RBF controller parameters. • Reduce the number of controllers used for synchronizing, improve the robustness of the synchronization system to noise, and a flexible and straightforward chaotic synchronization controller design. [ABSTRACT FROM AUTHOR]

Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of event-triggered optimal control for saturated nonlinear systems with full state constraints. A smooth function is defined to map the constrained states, then the considered system can be transformed into a state unconstrained system with unknown approximate errors. In addition, a novel event-triggered mechanism is proposed via an adaptive dynamic programming algorithm, which can obtain the optimal control law without constructing the so-called event-triggered HJB equation. Moreover, in order to conquer the difficulty caused by the persistence of excitation conditions, the experience replay technique is utilized to design the critic update law. Meanwhile, it is demonstrated that all signals are uniformly ultimately bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

This paper pays attention to the output tracking control problem of nonlinear systems where the output is uniquely measurable and subject to an intermittent constraint. A multiplicative transformation based on the shifting-replaying function is introduced together with barrier Lyapunov function to solve the intermittent output constraint. A state observer independent of the matching condition of control gains is designed via the non-uniform state transformation to relax the assumption of full-state measurability. By virtue of the estimated states, we propose an output feedback controller that only involves one fuzzy adaptive parameter to restrain the effect of unknown system nonlinearities. Through Lyapunov stability analysis, it is proved that the proposed controller can make all signals in the closed-loop system remain semi-globally uniformly ultimately bounded. Two simulation examples are provided to verify the effectiveness of the proposed method, and also the superiority over the existing ones. [ABSTRACT FROM AUTHOR]

This study investigates event-triggered (ET) mechanism-based sequential fusion filtering for nonlinear multi-sensor systems with composite correlated noise and random packet dropout. Composite correlated noise means that the observation noise at the same time is correlated, while the observation noise is also correlated with the process noise at the previous and the same instants. To minimize the energy loss within the system, the ET mechanism is used to reduce the communication rate of the sensors. The equation for the local filtering process is derived based on whether the ET mechanism has been triggered. To improve the accuracy of the filter, a noise estimator for local observations is developed using the ET mechanism. A two-step prediction method is used to calculate the estimate state vector of the main filter for time updating. In this paper, the sequential fusion filtering algorithm under the Bayesian framework is derived to solve the nonlinear systems with above problems, and the numerical implementation of the algorithm is given by the square-root cubature Kalman filter (SCKF). Finally, simulation experiments demonstrate that the developed algorithm enables a reduced communication rate of the sensor system while maintaining powerful filter estimation performance. [ABSTRACT FROM AUTHOR]

This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy neural networks (T2FNNs) have gained popularity due to their processing ability for high uncertainty. However, concerned with the high-dimensional problems of nonlinear systems, the interpretability of individual T2FNNs is weak due to the exponential growth of fuzzy rules. To deal with this problem, an information orientation-based modular T2FNN (IO-MT2FNN) is developed to improve its interpretability in this paper. First, an information entropy-based decomposition method is designed to divide the original input space into three sub-spaces, namely edge, local and global regions. Then, the information with different attributes is separated to provide an unambiguous interpretation. Second, the independent module describing these regions with type-2 fuzzy sets is embedded in the membership function layer of IO-MT2FNN to represent the coupling relationship between regional information in an interpretable way. Third, an information mapping strategy is introduced with low-order Gaussian kernel matrices, instead of a high-order mapping matrix, to extract the features from the allocated information in each module, which enables IO-MT2FNN to achieve a compact topology through dimensionality reduction. Finally, the simulations demonstrate that the proposed IO-MT2FNN can compete with the advanced approaches in terms of interpretability for the prediction of high-dimensional and complex systems. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive event-triggered (AET)-based path following controller design problem for a networked autonomous vehicle, where the limited networked bandwidth, system nonlinearities and uncertainties are considered. The polytopic model is proposed to construct a linear parameter varying (LPV) system for the nonlinear vehicle system. Taking into account the effects of event trigger on the path following performance, an improved AET mechanism is designed to achieve a balance between efficient communication and accurate path following requirements. Sufficient conditions are developed to guarantee that the closed-loop system is exponentially stable with an H ∞ performance index being satisfied. In addition, a co-design method with less conservatism is derived to obtain the event-triggered weight matrix and output feedback controller gain matrix simultaneously. Finally, simulation results verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L 2 − L ∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (C S T R). [ABSTRACT FROM AUTHOR]

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposed an event-triggered adaptive fuzzy prescribed time control strategy for a class of nonlinear systems with uncertain external disturbances and unknown virtual control coefficients under prescribed performance. A novel time-domain mapping technique is proposed to transform the prescribed time tracking control problem into an asymptotic convergence problem. An observer is designed to estimate for the external disturbance and fuzzy approximation error of fuzzy logic systems (FLSs). The problem of "explosion of complexity" is addressed by applying dynamic surface control (DSC) technique to backstepping. An adaptive fuzzy event-triggered strategy is designed using the Lyapunov stability theorem. This strategy ensures that, after time-domain mapping, the tracking error asymptotically converges to zero. Additionally, there is no Zeno behavior and all system signals are bounded. Finally, the effectiveness of the proposed scheme is verified through three simulation examples. [ABSTRACT FROM AUTHOR]

The finite-time distributed state estimation (DSE) problems based on sensor network for discrete-time nonlinear systems are considered in this paper. Considering the uncertainty of the target maneuvers, the interactive multiple models (IMM) based distributed estimation framework is established by local filter and consensus fusion. In the proposed distributed algorithm, partial of the output of the system can be collected by some sensors and the sensor network is supposed to be collectively observable. According to the consensus protocol, the final estimate results are obtained by fusing local estimate results of each sensor after the consensus fusion stage. The distributed estimate results can be obtained with finite-time when the consensus fusion step is larger than the diameter of the network, and the convergence rate of estimate error of the proposed distributed estimate algorithm can be guaranteed. Besides, the existence of the lower and upper bounds of the error covariance matrix are proved with some necessary assumptions. Finally, numerical simulation example is given for tracking the target with different maneuvers. [ABSTRACT FROM AUTHOR]

This paper presents a model reference adaptive control (MRAC) system for nonlinear, time-varying, hybrid dynamical plants affected by modeling uncertainties. This system is unique because, in addition to regulating the trajectory tracking error to zero, it allows the user to set the rate of convergence of the tracking error between consecutive resetting events. This proposed result has been possible by leveraging an auxiliary trajectory tracking error dynamics to accelerate convergence of the trajectory tracking error according to the two-layer MRAC framework. The resetting logic of both the reference model and the auxiliary trajectory tracking error dynamics bound variations in the trajectory tracking error due to undesired resetting events in the plant dynamics. The resetting events of the reference and auxiliary model also reduce the trajectory tracking error whenever some dwell-time condition is met. Finally, the resetting logic of both the reference model and the auxiliary trajectory tracking error reduces the control effort at isolated time-instants. Three numerical examples demonstrate the applicability of the proposed result as well as their advantages over alternative adaptive control techniques for nonlinear, time-varying, hybrid dynamical plants as well as classical MRAC. [ABSTRACT FROM AUTHOR]

This paper studies a distributed extended state observer design and dual-side dynamic event-triggered output feedback (DEOF) anti-disturbance control for interconnected systems (ISs) subject to quantization and multi-source disturbances. First, two novel dual-side dynamic event-triggered mechanisms (DETMs) are proposed to alleviate data transmission in both sensor-to-observer (S-O) and controller-to-actuator (C-A) channels. In addition, the DETM in S-O channel is related to the quantization parameter such that a trade-off between triggering frequency and quantization density can be achieved. Second, by using the transmitted system outputs, a distributed extended state observer is constructed to estimate system states and disturbances. Then based on the outputs of distributed extended state observer, a dual-side DEOF H ∞ controller is designed, which can compensate and attenuate two types of disturbances. Subsequently, some sufficient conditions are derived to guarantee system states and estimation errors converge to zero and system output satisfies H ∞ performance. Finally, a numerical simulation is provided to demonstrate the obtained results. • A distributed extended state observer for ISs is designed based on a novel DETM and a logarithmic quantizer. • A DETM containing the quantization parameter is designed such that a trade-off between event-triggered and quantization can be acquired. • A dual-side DETMs in both S-O and C-A channels are proposed to further save communication resources. [ABSTRACT FROM AUTHOR]

This paper suggests a unified tracking control scheme for systems suffering from unknown control direction and preassigned performance requirement. Distinguished from the existing Nussbaum function-based control methods, the presented approach achieves a unified control framework that encompasses the asymptotic or finite-time stability by introducing sliding mode technique when the nonlinear systems suffer from the unknown control direction issue. Two kinds of stabilities can be obtained only via choosing specific functions. Moreover, the suggested control approach can also deal with the changing of control direction. The stability is analyzed, and the total method rigorously guarantees the tracking errors' required performance criterion. The simulation results of the second order inverted pendulum model serve as verification of the proposed method. Furthermore, as an alternative application scenario, the attitude tracking issue of hypersonic vehicles is dealt with by the presented method subjected with the time-varying control coefficient. • The proposed approach achieves a unified control framework under the unknown control direction. • The control approach rigorously guarantees the tracking errors' required performance. • The simulation results serve as verification of the proposed method. [ABSTRACT FROM AUTHOR]

Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities. • We construct a neuron-inspired circuit model with indirect interactions involving energy. • The neuron-like excitability and bi-stability are identified in the neuron-inspired circuit. • The neuron-inspired circuit can reproduce excitability as same bifurcation mechanism as the HH neuron. • Stability conditions of the neural network are deduced by stability analysis. • Multistability is triggered in the neural network with different coupling matrix. [ABSTRACT FROM AUTHOR]

Pulsation is a universal phenomenon in all disciplines of nonlinear science, which generally exhibit various nonlinear soliton dynamic modes in nonlinear optics. With the emergence of real-time spectral measurement technology, a new phenomenon of optical soliton pulsation, "invisible" soliton pulsation, has gradually attracted researchers' attention. In this paper, by solving the coupled Ginzburg–Landau equation, we have discovered the partially "invisible" pulsation phenomenon of asymmetric soliton molecules (SMs) composed of two unequal-intensity pulses in a normal-dispersion Mamyshev oscillator for the first time. It is indicated that the fluctuation periods of each internal pulse in asymmetric SMs in terms of peak power, energy, and relative phase difference are all four roundtrips. However, the oscillation period of asymmetric SMs energy is two roundtrips, only half of the above period. Further research shows that the oscillation of the relative phase difference between two internal pulses in SMs is related to the variation of their intensity difference, which can also affect the position change of the spectral modulation peak. This work will enrich the research on "invisible" soliton pulsation and is of great significance for promoting the development of nonlinear dissipative systems. • We studied the pulsating dynamics of soliton molecules in a Mamyshev oscillator. • We discovered the partially "invisible" pulsation of asymmetric soliton molecules. • The total energy period of asymmetric soliton molecules is half of each inside pulse. • The "invisible" pulsation is caused by the intensity difference of the inside pulses. [ABSTRACT FROM AUTHOR]

Understanding and controlling neural network synchronization is crucial for neuroscience in revealing brain functions and addressing neurological disorders. This study explores the innovative use of dynamic learning of synchronization (DLS) technology to enhance synchronization within neuronal networks. Using the Hodgkin-Huxley model across various network topologies, including Erdős-Rényi random graphs, small-world, and scale-free networks, it dynamically adjusts external electrical excitation to study its effects on network synchrony. To further demonstrate the universality of DLS technology, this study also validates the main results using larger-scale networks and the Izhikevich and FitzHugh-Nagumo models. The research quantifies the enhancement of synchrony through DLS, using root-mean-square error (RMSE) and synchronization factors as metrics. Findings show that DLS effectively boosts network synchrony by dynamically adjusting external excitation in response to node differences, significantly in both small-world and scale-free networks, irrespective of synaptic connections. Furthermore, DLS demonstrates potential for targeted synchronization enhancement in specific region of network. This paper highlights DLS technology's effectiveness in modulating external excitation to improve complex neural network synchrony, providing new insights into neural synchronization and information transmission. • A dynamic learning of synchronization (DLS) technique is proposed. • Our DLS technique can improve neural network synchrony by adjusting external electric stimulation in real-time. • The study evaluates DLS effects across different network structures by using Hodgkin-Huxley model. • DLS offers potential for targeted synchronization enhancement in specific parameters region of network. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the exponential stabilization of stochastic nonlinear systems. Different from the single event-triggering mechanism in traditional deterministic/stochastic control systems, based on two stopping time sequences, we propose a double-event-triggering mechanism (DETM) to update control signals and make two different controls switch in order. Also, this novel DETM allows aperiodic time updating and guarantees a positive lower bound on the inter-event times. Together with this DETM, we introduce a switching control law that consists of a primary control and a secondary control for a non-switched stochastic system to obtain the exponential stabilization and boundedness results. Finally, an illustrative example with simulation figures is provided to demonstrate the obtained results. • A novel switching control is first established for a non-switched stochastic system. • The switching control generalizes the traditional periodic and aperiodic intermittent controls. • We first extend the single event-triggering mechanism to a double-event-triggering mechanism. • Zeno phenomenon is effectively avoided under the double-event-triggering mechanism. • Exponential stabilization and boundedness problems of stochastic nonlinear systems are solved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method. • An ESN adaptive controller is proposed for interconnected pure-feedback unknown nonlinear systems with finite-time stability. • The input saturation, actuators faults, triggering events and complexity explosion are dealt with using state transformation. • The adaptive laws of the ESN are derived for the first time using control-errors instead of tracking-errors. • The parameters of the adaptive laws are highly reduced due to the use of only one ESN regardless of system's order. [ABSTRACT FROM AUTHOR]

This paper studies the distributed state estimation problem for nonlinear systems with random transmission delays and transmission failures, and proposes a novel sequential hybrid consensus filtering algorithm. The covariance intersection method is used to reach consensus over priors, and the consensus on measurements is used to fuse the innovation information, which makes the proposed algorithm robust to transmission failures. A compensation scheme is proposed when there are one-step transmission delays. The consensus weight of the delayed information is derived, and with the compensation term, the local estimation accuracy is improved. Rather than waiting for all information from neighboring nodes, the proposed algorithm is implemented sequentially once information from a neighboring node is received during the consensus step. The rigorous theoretical performance analysis is presented, and the proposed algorithm is tested numerically on a single target tracking problem and a distributed navigation of satellite cluster problem. [ABSTRACT FROM AUTHOR]

Practical time-varying formation-containment tracking (TVFCT) issue for nonlinear multi-agent systems with general noise is researched in this paper. A neuro-adaptive practical TVFCT protocol is put forward, where neural networks (NNs) and parameter adaptive laws are developed for estimating the nonlinearities and compensating the upper bound of the time-varying formation (TVF) condition, respectively. Leaders are expected to achieve the predetermined TVF and followers are driven to move into the formation structure confined by leaders simultaneously. The whole formation position depends on the desired trajectory produced by a virtual-leader. General noise rather than white noise is investigated in the multi-agent systems. The noise-to-state-practically stability in probability (NSPS-P) criteria can be guaranteed by employing the Lyapunov theories combined random differential equations (RDEs). Numerical simulation results reveal the effectiveness of the developed protocols. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the p th moment exponential stability of impulsive random delayed nonlinear systems (RDNS) with average-delay impulses. Utilizing the average impulsive interval, average impulsive delay, and the Lyapunov method, we present several criteria for p th exponential stability in these systems under a novel condition, diverging from previous literature. Additionally, we explore the effects of delayed impulses, analyzing both destabilizing and stabilizing impulses. Our findings reveal the dual effects of time delay in impulses, which can potentially destabilize a stable system or stabilize an unstable one. • The p th moment exponential stability is investigates for impulsive RDNS. • Established stability criteria for impulsive RDNS with average-delay impulses. • Both continuous dynamics and impulses take time delay into account. • Average delayed impulses can stabilize unstable systems or destabilize stable ones. [ABSTRACT FROM AUTHOR]

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights' updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the zonotope-based interval estimation problem for event-triggered nonlinear systems with incrementally quadratic constraint and unknown-but-bounded uncertainties from process disturbance and measurement noise. Considering the restricted communication bandwidth, an event-triggered communication protocol is deployed in the sensor-to-observer channel, based on which an event-triggered observer is constructed for nonlinear systems having incremental quadratic constraints. A co-design method of nonlinear observer and event-triggered protocol is obtained to ensure the stability and ℓ ∞ index of the estimation error dynamic. Based on the designed event-triggered observer, a zonotope-based interval estimation algorithm is designed for the purpose of giving the intervals enclosing admissible values of system state. The mean value extension coalesce into natural interval extension is utilized to deal with the nonlinear transformation of system, and the enclosing zonotope of ellipsoid is introduced to tackle the extra uncertainties induced by event-triggered protocol. Lastly, the results of a simulation on a hyper-chaotic Chen system are provided to confirm the validity of the presented methodology. [ABSTRACT FROM AUTHOR]

This paper addresses the optimized leader–follower consensus control problem of nonlinear canonical dynamic multi-agent system (MAS). Since every agent is modeled in high-order dynamic, they contain the various state variables having derivative relations. Consequently, to attain the optimized consensus control, backstepping technique and reinforcement learning (RL) are combined together. In the first backstepping step, the virtual control is formulated to have the consensus error term consisting of neighbor agents' output states. In the last backstepping step, since the nonlinearity dynamic is arisen, the optimized actual control is derived by performing the critic-actor RL. It is worth mentioning that, in the traditional RL optimal control, the critic and actor updating laws are obtained by performing the gradient descent algorithm to square of the approximated Hamilton–Jacobi-Bellman (HJB) equation, which includes multiple nonlinearity items, as a result, the algorithm is very intricate. However, in this optimized consensus control, since the RL training laws are yielded in the light of negative gradient of a simple positive function that is relevant to the HJB equation, its algorithm is very simple. At the same time, it can also avoid the persistence excitation conditions. Finally, theory and simulation confirm the validity of this optimized consensus method. [ABSTRACT FROM AUTHOR]

This paper uses a prescribed-time event-triggered approach to explore the control of uncertain strict-feedback nonlinear systems with output constraints and an unknown time-varying control gain. The proposed method utilizes a universal barrier Lyapunov function (BLF) to ensure compliance with the output constraints. Furthermore, a technique known as congelation of variables is employed to handle the unknown time-varying control gain. Approximating the unknown dynamics using radial basis function neural network (RBFNN), a neural prescribed-time controller is designed based on the backstepping approach. Additionally, the event-triggered mechanism is employed to conserve computational and communication resources. With this scheme, all signals are guaranteed to converge to a compact set within the prescribed time frame. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithm. • The RBFNN is employed to approximate the uncertain dynamics. • A time-varying BLF is introduced to address the constraints on the tracking error. • The unknown control gain is tackled by a method known as congelation of variables. • A prescribed-time event-triggered approach achieves the controller design. [ABSTRACT FROM AUTHOR]

This paper studies the sliding-mode surface (SMS)-based approximate optimal control issue for a class of nonlinear multiplayer Stackelberg-Nash games (MSNGs). First, considering different roles of the players in MSNGs, a hierarchical decision-making process is expressed as designing different cost functions for the leader and the followers. Therein, the leader makes its decision preferentially with consideration of all followers, while each follower responds optimally to leader's strategy simultaneously via Nash games. Then, based on the sliding mode control technology, a novel robust control policy is proposed to solve the coupling Hamilton–Jacobi equations of nonlinear MSNGs. Subsequently, SMS-based critic network is utilized to approximate optimal control inputs for all players. Based on the Lyapunov stability theory, it is strictly proven that all signals of the closed-loop nonlinear systems are uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated via a simulation example. • The Stackelberg-Nash game (SNG) has one leader and multiple followers. • The SMC method is combined with optimal control design for SNG. • The robust control scheme applies only a critic network. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time stability (FTS) of equilibrium point of a class of fractional-order nonlinear systems (FONSs) described by Caputo fractional-order derivative (CFOD). The definition of finite-time equilibrium point (FTEP) is proposed for the FONSs, and it is proved that the CFOD of the FTEP is not constantly equal to 0. A sufficient and necessary condition on the FTEP is proposed. Based on the asymptotical stability and the method of the integral of unbounded integrand, two sufficient conditions on the FTS of the equilibrium point are provided. Consequently, the existence of finite-time stable equilibrium points in the FONSs is confirmed. Two examples are presented to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques. [ABSTRACT FROM AUTHOR]