Search

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]

• For the fast-varying delay, an improved analytical method based on Lyapunov-Krasovskii (LK) functionals is given by introducing and proving a new lemma, which is not only independent of the upper bound of time-varying delay, but also independent of the derivative of the time-varying delay. Hence, the developed analytical method greatly expands the application range of the LK functional. • For unknown nonconstant control coefficients, an output feedback control strategy based on the compensated system is proposed. As an intermediate link, the adaptive fuzzy system is introduced into the controller indirectly by the compensation system, so as to avoid the algebraic-loop problem. Hence, the cooperative design of the compensation system, the state observer and the controller is one of the innovations in this paper. • Considering the problems of state immeasurability and time-varying delay comprehensively, an adaptive fuzzy output-feedback control law is proposed based on an improved average dwell time, which relaxes the constraints between the LK functional of each subsystem in switched large-scale interconnected nonlinear systems. In this paper, an adaptive fuzzy decentralized output-feedback control is developed for the uncertain switched large-scale interconnected nonlinear system, which contains fast time-varying delays and unknown nonconstant control coefficients. By introducing and proving a new lemma, an improved analysis method is given based on the Lyapunov-Krasovskii (LK) functional, and it gets rid of the dependence of LK functional design on the bound of the derivative of the delay. Immeasurable states are estimated by co-designing the decentralized state observer and the innovative compensation system, which eliminates a widely adopted but strict assumption that the unknown control coefficient must be constant. By comprehensively designing the state observer, the compensation system and LK functionals, a novel adaptive fuzzy decentralized output-feedback control law is proposed, and stability of the closed-loop system is guaranteed theoretically based on an improved average dwell time. Finally, the effectiveness is further verified by complete simulation experiments. [ABSTRACT FROM AUTHOR]

The fixed-time tracking control issue is investigated for a class of high-order nonlinear delayed systems subject to mismatched disturbances in this paper. Wherein, the fuzzy logic system is applied in dealing with the nonlinear functions and the power integrator technique is appropriately introduced to address the high-order terms in the considered system. Different from the conventional methods of using the Lyapunov-Krasovskii functional approach to cope with the delayed terms in the previous work, the adaptive backstepping method is utilized in this paper. The main purpose of the addressed control problem is to design a suitable adaptive fuzzy fixed-time controller such that the closed-loop system is stable and guaranteed to be bounded in a fixed-time interval. Subsequently, the specific control law is deduced through the inductive method, and the upper bound on the settling time for the fixed-time control is given. Finally, the simulation examples are given to illustrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive fixed-time tracking control problem for a class of stochastic nonlinear systems with constrained states and input saturation. By utilizing a barrier Lyapunov function (BLF), the issue caused by constrained states is settled. Simultaneously, a smooth function is constructed to approximate input saturation and the unknown nonlinear function is approximated by neural networks (NNs). In view of the fixed-time tracking control problem of stochastic nonlinear systems, a fixed-time stability lemma for stochastic nonlinear systems has been established and proved. Under the designed controller, the closed-loop system is semi-globally fixed-time stable in probability (SGFSP), and all the states are constrained within a compact set. Moreover, the controlled system in this paper achieves equilibrium within a fixed-time internal. Lastly, the presented method is verified by a simulation example. [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]

In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network's ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs). [ABSTRACT FROM AUTHOR]

In this paper, we propose a fault diagnosis (FD) approach for a class of nonlinear uncertain systems based on the deterministic learning approach (DLA). Specifically, an adaptive learning observer is constructed, in which the adaptive neural networks (NNs) are constructed to approximate the unknown system dynamics under normal and fault modes. Based on the strictly positive real (SPR) condition, the convergence of the state estimation can be guaranteed. When the system is undergoing a periodic or periodic-like (recurrent) motion, the states of the observer will also become recurrent. Thus through DLA, the partial persistent excitation (PE) condition of the associated subvectors of NNs is satisfied. By utilizing the partial (PE) condition, the uniformly completely observable (UCO) property of the identification system is analyzed and the exponential convergence condition of the identification system is derived. Under this condition, the unknown dynamics under normal and fault modes can be accurately identified along the system trajectory. And by utilizing the knowledge obtained in the identification phase, the fault can be detected in the diagnosis phase. The main attraction of this paper lies in the analytical result, which shows that the exponential convergence condition of the learning observer not only depends on the observer gain matrix, but also depends on the PE level of the regressor subvector of NN. Simulation results are included to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present a connectivity-preserving performance function approach for the distributed output-feedback synchronized tracking of uncertain heterogeneous nonlinear multiagent systems in a nonstrict-feedback form. Compared with existing output-feedback cooperative control results using neural networks, this paper contributes to developing a universal output-feedback synchronized control methodology that uses a connectivity-preserving performance function to ensure both initial network connectivity and preselected synchronization performance with a designable convergence time. To this end, a neural-network-based adaptive observer for each follower is designed to ensure the boundedness of estimation errors of unmeasurable states. Then, local event-triggered synchronized trackers using only relative output information and the connectivity-preserving performance function are constructed to guarantee the closed-loop stability in a low-complexity sense, where no adaptive neural networks and command filters are not required in the local trackers. Finally, a purely academic example and a practical platoon-control problem of multiple uncertain vehicular systems are considered to clarify and verify the proposed connectivity-preserving performance function approach in the simulation. [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]

The state-dependent Riccati equation (SDRE) unveils a nonlinear optimal control approach; the method is sensitive to uncertainty and disturbance that provokes the necessity of precise modeling and omitting disturbance from the model and environment which is occasionally impossible. In this paper, a robust state-dependent Riccati equation is introduced using only the pure SDRE itself. Lyapunov's second method for stability analysis is used to extract two tuning rules for weighting matrices of the robust approach for handling both matched disturbance and parametric uncertainty. A fourth-order differential equation is simulated to show the effectiveness of the suggested method and the results were compared with conventional SDRE. The robust version could handle the matched disturbance with a steady-state shift from the equilibrium point where the conventional SDRE failed. Additionally, a comparison and detailed analysis have been performed between the proposed design and sliding mode control. • A robust SDRE design is proposed based on the defined bound of the uncertainty in the weighting matrices. • The stability of the controller is proved using the Lyapunov method to find the weighting matrices. • A fourth-order nonlinear system is simulated as an example of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a class of interconnected systems is considered, where the nominal isolated subsystems are fully nonlinear and non-minimum phase. A decentralized Extended Kalman Filter-Extended High Gain Observer (EKF-EHGO) is designed to observe the system states. Then, a systematic backstepping design procedure is employed to develop a novel decentralized robust adaptive output feedback control, in which the adaptive law is designed to counter the effects of the interconnections and uncertainties. The proposed decentralized dynamic output feedback control scheme can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Both interconnections and uncertainties are allowed to be unmatched and bounded by an unknown high-order polynomial, which is a more general form when compared with existing work. Two MATLAB simulation examples are used to demonstrate the effectiveness of the proposed method including a system comprising translational oscillator with rotating actuator (TORA) sub-systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with distributed fixed-time containment control for nonlinear multiagent systems with actuator faults via static and dynamic event-triggered strategies. A distributed fixed-time static event-triggered fault-tolerant controller is developed by employing the sign function, which eliminates the requirement for continuous control signal updates. To address the chattering phenomenon caused by the sign function, a distributed saturation controller is presented to enhance the control performance. To further reduce energy consumption and frequency of controller updates, a dynamic event-triggered strategy with an auxiliary parameter is proposed for each agent to dynamically regulate its threshold. The control scheme guarantees that the containment control objective is achieved within the settling time, and does not exhibit Zeno behavior. The effectiveness of the proposed control scheme is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time (FT) adaptive output feedback control for a class of nonlinear systems with asymmetric state-function constraints and unknown external disturbances. Incorporating the asymmetric barrier Lyapunov function (BLF) into the backstepping technique, a new control approach is proposed to ensure that all states do not cross the constraint boundary. With the help of the command filter, the explosion of complexity induced by repeated differentiations of virtual controllers is eliminated, and the corresponding compensation system is used to offset the filter error. Meanwhile, the fuzzy logic system (FLS) and fuzzy state observer are employed to approximate unknown nonlinear functions and estimate unmeasurable states respectively. For effectively conserve communication resources, a novel adaptive event-triggered controller is proposed such that all signals of the closed-loop system are bounded, the tracking error converges to a small neighborhood containing the origin in finite time. Finally, the feasibility of the fabricated control scheme is verified with two examples. [ABSTRACT FROM AUTHOR]

This paper presents a fixed-time adaptive resilient control framework based on reinforcement learning (RL), mismatch disturbance observer and nonsingular fast terminal sliding mode scheme for nonlinear cyber-physical systems (CPS) to enhance cyber-security under False Data Injection (FDI) attacks, as well as match and mismatch disturbances. The RL algorithm contains an actor-critic neural network (NN) in which the actor NN is employed to estimate the uncertainty while the critic NN is applied to evaluate the performance cost function. Next, to compensate the detrimental effects of attacks and mismatch disturbances, a new sliding mode-based adaptive disturbance observer is designed. To achieve high precision trajectory tracking within a fixed-time interval, a nonsingular fast terminal sliding mode scheme is designed. This scheme ensures fixed-time convergence of the tracking error and facilitates disturbance attenuation and attack mitigation which are the key features of the proposed fixed-time secure control strategy. Finally, the fixed-time stability analysis of is performed through Lyapunov theory. Results reveal the effectiveness of the proposed resilient control for wind turbine system as the nonlinear CPS. [ABSTRACT FROM AUTHOR]

• It proposes a new fault tolerant control sheme in HVs. • The validity of effectiveness of the fault tolerant control is verified by multiple sets of experimental data. • Prove the fault extended state observer and whole FTC sheme converging in finite time. • Compensate the effect of external attitude disturbance, actuator faults and saturation on the system. This paper proposes a radial basis function neural network and the actuator fault extended state observer based fast non-terminal sliding mode fault-tolerant control scheme for hypersonic vehicles (HVs) system. The proposed scheme can cope with actuator faults, actuator saturation, parameter uncertainties, and external disturbances for HVs systems, without relying on redundancy as some passive FTC methods do. Moreover, an anti-windup compensator is designed to mitigate the input saturation effects. Furthermore, the finite-time stability of the attitude angle of the HVs system is proved by Lyapunov's theorem. Numerical simulations validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

• A novel event-triggering mechanism and three dynamic gains are introduced to compensate uncertainty and execution error. • It overcomes difficulties from unknown polynomial growth rate, unknown large measurement sensitivity and time-delay. • It proves that all the signals are bounded, the states converge to zero asymptotically, and the Zeno behavior is excluded. In this paper, the problem of adaptive event-triggered output-feedback stabilization is addressed for a class of switched nonlinear systems with time-delay and output measurement sensitivity. With the assistance of the dynamic high gain technology and a novel event-triggered control mechanism, we overcome the design complexities arising from unknown polynomial growth rate with respect to the output, unknown large measurement sensitivity, unknown time-varying control coefficient and time-delay. Then, an effective constructive method is provided to design switched observers and a common event-triggered controller. Through introducing two key matrix inequalities and constructing a common Lyapunov-Krasovskii functional, sufficient conditions are given to get rid of Zeno behavior, and ensure that all the signals are bounded and the closed-loop system states converge to zero under arbitrary switchings. Two simulation studies are conducted for verifying the effectiveness of proposed scheme. [ABSTRACT FROM AUTHOR]

The distributed-order fractional calculus (DOFC) is a generalization of the fractional calculus which its application can be found in viscoelasticity, transport processes and control theory. In the current paper, a system of time fractional distributed-order diffusion equation is investigated, numerically. In the first stage, the time derivative is approximated by a finite difference formulation. The integral terms are approximated by the numerical integration. Then, a semi-discrete scheme is constructed by this procedure. In the second stage, The stability and convergence of the time-discrete outline are analyzed by the energy method. In the third stage, the space derivative is discretized by the compact integrated radial basis function (CLIRBF) as a truly meshless method. Also, the numerical procedures are performed on regular and irregular computational domains. The numerical experiments verify the ability, efficiency and accuracy of the developed numerical formulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the output feedback tracking control of a high-order nonlinear system with denial-of-service (DoS) attacks and exogenous disturbances. A radial basis function neural network (RBFNN)-based state observer is employed to estimate the system states. A new nonlinear filter with adaptive regulation is developed to eliminate the impacts of perturbed factors such as RBFNN approximation errors and disturbances. Constituting with filtering operation and backstepping control technique, a RBFNN-based security controller is constructed to suppress the influences of perturbations and DoS attacks based on the observation signals. The uniformly ultimately bounded output tracking result is established by using the security control signals via Lyapunov criterion in the cases of DoS attacks, nonlinearities, and disturbances. Comparative results are provided to validate the efficiency of the developed RBFNN-based observation and security control strategies of a nonlinear system. [ABSTRACT FROM AUTHOR]

In previous research on fault switching of redundant actuators using monitoring modules, the interference of sensor faults on monitoring results has not received enough attention. In this paper, a new fault-tolerant control (FTC) method combining adaptive compensation and active switching is proposed for a class of uncertain nonlinear systems with backup actuators against actuator and sensor faults. While using command filtered backstepping to reduce computational burden, a direct adaptive compensation scheme is designed to ensure that sensor faults within tolerable bounds do not trigger actuator switching. Based on this, a new lumped monitoring function (MF) containing prescribed performances and tolerable sensor fault bounds is designed to detect and isolate faulty actuators and ensure that the tracking error always satisfies prescribed transient and steady-state performances. Two simulation cases are used for illustrating the proposed method. It is proved that the proposed method can effectively reduce the interference of sensor faults on actuator fault detection and improve the accuracy of actuator switching. [ABSTRACT FROM AUTHOR]

This paper proposes a nonsmooth funnel function (NFF)-based model-free adaptive sliding-mode control strategy for the discrete-time nonlinear systems with unknown dynamics and asymmetric constraints. The dynamic linearization model of the nonlinear systems with unknown dynamics is obtained online only using the input/output data, which is combining with the designed NFF-based discrete-time sliding-mode surface to guarantee asymmetric constraints of the tracking error. In the proposed NFF, the coordinate transformation for asymmetric constraints simplifies the controller design, and the nonsmooth parameter can improve the transient and steady-state performances of the tracking error. The control consumption is further reduced by a proposed time-varying weighting factor-based cost function in the controller design. Furthermore, parameter selections of performance boundaries and the sliding-mode surface are given, and the performance margin (the minimum distance from the tracking error to the preset boundaries) is proved theoretically. Simulation and experimental results verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The adaptive tracking problem for a class of strict-feedback switched nonlinear systems with output constraints, quantization input, distributed time-varying delays and external disturbances is studied in this paper. Firstly, we introduce the hyperbolic tangent function to handle the quantized signal in the design of the controller. For the nonlinear term and distributed time-varying delay of the system, the integral term is introduced into the candidate functional to compensate it. Secondly, based on Dynamic Surface Control (DSC) technique and Barrier Lyapunov function (BLF) method, an adaptive controller is designed to guarantee the stability of the controlled closed-loop system, and the system tracking error can converge to the origin without violating the constraints. Finally, simulation results verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered adaptive control for a class of strictly-feedback stochastic nonlinear systems. The output dead zone and time-varying full-state constraints are considered in the controller. Firstly, time-varying barrier Lyapunov functions (TVBLFs) are introduced to address problems of time-varying state constraints. Then, the Nussbaum-type function is used to compensate for the influence of the output dead zone. The problem of state constraint is well solved when the system's output signal is affected by the dead zone, which satisfies a wider application space. In addition, a new relative threshold of the event-triggered control (ETC) scheme is considered to save communication resources, and the Zeno behavior is excluded. This scheme makes the trigger interval more flexible and optimizes the performance of the controller. Moreover, the error compensation signals reduce the filtered errors and simplify the algorithm. Simultaneously, an adaptive tracking controller with the backstepping technique is designed so that all signals in the closed-loop system are bounded and the tracking error converges to a small residual set of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It $\hat {o}$ ’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results. [ABSTRACT FROM AUTHOR]

For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system. [ABSTRACT FROM AUTHOR]

• In the framework of finite-time command filter control, this paper constructs a quadratic function in the controller. Compared with [23, 24, 25], the presented adaptive finite-time control algorithm not only solves the "explosion of complexity" problem effectively, but also circumvents the singularity problem. • In contrast to the literatures on finite-time control [43, 44, 45], the cases of faults happening during transmission phase of system are rarely considered. Moreover, nonlinear faults may exist in many real systems, which necessitates the design of fault-tolerant controllers to enhance the system reliability and guarantee consistent control performance. In this paper, nonaffine nonlinear faults are taken into account, which is more complex than linear faults studied in [37, 39, 46]. • Different from the results [28, 29, 47] which used the trial-and-error method to validate the observation gain matrix, this paper skillfully introduces the differential mean value theorem and the convex combination theorem to transform the acquisition of the observation gain matrix from solving a nonlinear matrix inequality to solving a set of LMIs. Meanwhile, the solvability of LMIs guarantees the stability of the observer and simplifies the algorithm. The present work deals with the consensus issue for nonlinear multiagent systems (MASs) subject to nonaffine nonlinear faults and unmeasurable states. First, the Butterworth low-pass filter (BLPF) is exploited to eliminate the algebraic loop problem arising from nonaffine nonlinear faults. In light of the convex combination theory, a neural observer is established to estimate the unmeasured states, which improves the efficiency of solving the observer gain. Then, with the help of the adaptive backstepping algorithm, an observer-based neural finite-time control protocol is proposed in which a quadratic function is constructed to circumvent the singularity problem. The finite-time stability criterion and Lyapunov stability theorem are utilized to demonstrate that all signals of the closed-loop system are bounded in finite time. Finally, a simulation experiment is applied to show the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

• The RODAs and DETM are both considered in FTFD problem of conic-type nonlinear systems. • A finite-time fault detection filter is proposed to handle conic-type nonlinearity and RODAs. • New sufficient criterion is given to achieve the finite-time stochastic stability with H ∞ requirements. The paper is concerned with the finite-time fault detection (FTFD) problem for a class of delayed networked systems subject to conic-type nonlinearity and randomly occurring deception attacks (RODAs) via dynamic event-triggered mechanism (DETM). The nonlinear function with the conic-type constraint is limited to a known hypersphere with uncertain center. Moreover, a variable governed by Bernoulli distribution is introduced to characterize the RODAs phenomenon. In order to reduce unnecessary communication transmissions, a DETM is considered in the design of finite-time fault detection filter (FTFDF) for the addressed networked systems with time-delays. This paper focuses on the design of an FTFDF via the DETM to ensure the finite-time stochastic stability of error dynamics system with satisfactory the prescribed H ∞ performance. Moreover, the desired FTFDF parameter matrices are obtained by solving linear matrix inequalities. In the end, a simulation example is employed to illustrate the validity of the proposed FTFD method. [ABSTRACT FROM AUTHOR]

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ ∈ (0 , 1 ] , we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O (h m + ɛ τ 2) up to the long time at O (1 / ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE. [ABSTRACT FROM AUTHOR]

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach. [ABSTRACT FROM AUTHOR]

This paper deals with state estimation for a class of Lipschitz nonlinear systems under a time-varying disconnected communication network. A distributed observer consists of some local observers that are connected to each other through a communication network. We consider a situation where a communication network does not remain connected all the time, and the network may be caused by intermittent communication link failure. Moreover, each local observer has access to a local measurement, which may be insufficient to ensure the system's observability, but the collection of all measurements in the network ensures observability. In this condition, the purpose is to design a distributed observer where the estimated state vectors of all local observers converge to the state vector of the system asymptotically, while local observers exchange estimated state vectors through a communication network and use their local measurements. According to theoretical analysis, a nonlinear and a robust nonlinear distributed observer exist when in addition to the union of all communication topologies being strongly connected during a time interval, the component of each communication graph is also strongly connected during each subinterval. The existence conditions of the distributed observers are derived in terms of a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the presented method is numerically verified using some simulation examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the attack detection and security control problem for discrete-time nonlinear cyber-physical systems (CPSs) under false data injection (FDI) attacks, which can bypass the traditional error detection mechanism. With the help of the T–S fuzzy models, a novel robust extended state observer with H ∞ performance is proposed to estimate this kind of attack. The attacks are included inside the observer as an internal state variable and the estimation of the FDI attack can be obtained from the outputs of the observer. By utilizing the observation of the FDI attack, a compensator is designed to negate the attack. Additionally, a controller is proposed to bring on the attack ineffective. Finally, simulation examples are given to illustrate the effectiveness of the developed schemes. [ABSTRACT FROM AUTHOR]

In this paper, the optimal model reference adaptive control (MRAC) problem is studied for the unknown discrete-time nonlinear systems with input constraint under the premise of considering robustness to uncertainty. Through an input constraint auxiliary system, a new adaptive-critic-based MRAC algorithm is proposed to transform the above problem into the optimal regulation problem of the auxiliary error system with lumped uncertainty. In order to realize the chattering-free sliding model control for the auxiliary error system, an action-critic variable is introduced into the adaptive identification learning. In this case, the closed-loop control system is robust to the disturbance and the neural network approximation error. The uniformly ultimate bounded property is proved by the Lyapunov method, and the effectiveness of the algorithm is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Purpose: The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be defined in the same simplified way as the other parameters due to the complexity of the physical effects. The purpose of this paper is to develop a mathematically stable approach for damping resonances in nonlinear ODE systems. Design/methodology/approach: Modifying the original ODE using the eigenvalues and eigenvectors of a linearized state leads to satisfying results. Findings: An iterative approach is presented, how to modify the original ODE, to achieve a well-damped solution. Practical implications: The method can be applied for every physical resonating system, where the model complexity prevents the determination of the damping. Originality/value: The iterative algorithm to modify the original ODE is novel. It can be used on different fields of the physics, where a second-order ODE is describing the problem, which has only measured or empirical damping. [ABSTRACT FROM AUTHOR]

In this paper, an observer with exponential time-varying gain is proposed for a class of nonlinear systems in Takagi–Sugeno form with both continuous-time and aperiodic sampled outputs. The proposed observer consists of two parts: one related to the continuous-time outputs and one related to the discrete outputs. Sufficient conditions involving a tuning parameter and the maximum allowed sampling time are derived in terms of quasi linear matrix inequality with respect to a scalar to ensure asymptotic convergence of the observer on the basis of Lyapunov–Krasovskii functional and H ∞ approach. Numerical simulations are provided to show the benefits of the proposed observer. Some comparisons with the high gain continuous-discrete observer and fuzzy observer with constant gain are provided to illustrate the interest of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a security consistent tracking control scheme with event-triggered strategy and sensor attacks is developed for a class of nonlinear multi-agent systems. For the sensor attacks on the system, a security measurement preselector and a state observer are introduced to combat the impact of the attacks and achieve secure state estimation. In addition, command filtering technology is introduced to overcome the "complexity explosion" caused by the use of the backstepping approach. Subsequently, a new dynamic event-triggered strategy is proposed, in which the triggering conditions are no longer constants but can be adjusted in real time according to the adaptive variables, so that the designed event-triggered mechanism has stronger online update ability. The measurement states are only transmitted through the network based on event-triggered conditions. The proposed adaptive backstepping algorithm not only ensures the security of the system under sensor attacks but also saves network resources and ensures the consistent tracking performance of multi-agent systems. The boundedness of all closed-loop signals is proved by Lyapunov stability analysis. Simulation examples show the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of event-triggered integral sliding mode control (ISMC) for the perturbed nonlinear based-Takagi-Sugeno (TS) fuzzy systems. To reduce the chattering introduced by the unmatched disturbances, a disturbance observer is designed to get the estimated unmatched disturbances. To further reduce the computational burden and communication resources, compared with previous studies, two types of sliding surfaces are established. The time-triggered-based sliding surface which is used to ensure the reachability of the system states and the event-triggered-based sliding surface that is presented to calculate the control law, directly which benefits from less updates and consequently, less chattering that enhance the system performance. Moreover, the suggested control scheme is proposed based on asynchronous trait, i.e. , the premise variables of the controller are in different time scale with the fuzzy systems which also leads to communication resource reduction. As a key issue in event-triggered control, it is ensured that the proposed controlled system is Zeno-free along the implementation. By the Lyapunov theory, the appropriate conditions for the ultimate boundedness stability (UBS) of the closed-loop system with a prescribed H ∞ performance are derived in new offline LMIs. In order to illustrate the effectiveness of the suggested event-triggered integral sliding mode control, the Rossler system and track-trailer system are simulated and the obtained results are evaluated with the existing methods. [ABSTRACT FROM AUTHOR]

This paper proposes a disturbance observer-based neural adaptive stochastic control approach for the attitude control system of a class of Kinetic Kill Vehicles (KKVs) with unmeasured states and full state constraints. First, a one-one mapping is applied to transform the attitude control system with state constraints into a nonlinear novel system without any constraint. As a result, the control objective is changed into the boundness of the novel system states. Furthermore, the disturbances existing in the system are effectively estimated and eliminated by the nonlinear disturbance observer as well as the radial basis function neural networks (RBFNNs). Moreover, due to the dynamic signal, the dynamic uncertainty induced by the unmeasured states with an unknown dynamic is compensated appropriately. Utilizing the stochastic Lyapunov process, the boundness of all the signals in the system can be proven and the state constraints are satisfied. Finally, two groups of simulations are conducted, which demonstrate the remarkable performance of the proposed algorithm under different working conditions and highlight the advantages compared with existing studies. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems' dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time static output feedback control for a class of nonlinear singular systems. Finite-time stability criterion for the closed singular systems is proposed by static output feedback technique. Based on the properties of structure of the singular system, static output feedback control gain is obtained by using singular value decomposition technique. Meanwhile, different from the existing results of normal systems, the presented scheme reduces the conservatism and complexity during the calculation process. Furthermore, static output feedback H ∞ controller is designed and finite time stability criterion is proposed for the nonlinear singular systems with external disturbance. Finally, the applicability and effectiveness of the proposed strategy are illustrated by a circuit system simulation. [ABSTRACT FROM AUTHOR]

This paper studies the PWM control problem of a class of nonlinear systems. During a modulation period, the PWM control signal maintains a pulse waveform with tunable width and fixed magnitude. The PWM control only possesses finite states, and has relatively limited control capability. This causes the degradation of system performance, and even the instability when implementing into a nonlinear system. We will introduce a novel method to design both the state feedback stabilizer and the output feedback stabilizer for strict-feedback nonlinear systems via the PWM control. The system performance is analyzed in a novel framework and the stability criteria is derived to ensure the system convergence. At last, two examples are considered to illustrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]