Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems

An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

This paper studies deterministic and stochastic fixedtime stability of autonomous nonlinear discrete-time(DT)systems.Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified.Extensions to systems under deterministic perturbations as well as stochastic noise are then considered.For the former,sensitivity to perturbations for fixed-time stable DT systems is analyzed,and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions.For the latter,sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented.The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems,and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems.Illustrative examples are given along with simulation results to verify the introduced results.

Online optimal control of nonlinear discrete-time systems using approximate dynamic programming

In this paper,the optimal control of a class of general affine nonlinear discrete-time(DT) systems is undertaken by solving the Hamilton Jacobi-Bellman(HJB) equation online and forward in time.The proposed approach,referred normally as adaptive or approximate dynamic programming(ADP),uses online approximators(OLAs) to solve the infinite horizon optimal regulation and tracking control problems for affine nonlinear DT systems in the presence of unknown internal dynamics.Both the regulation and tracking controllers are designed using OLAs to obtain the optimal feedback control signal and its associated cost function.Additionally,the tracking controller design entails a feedforward portion that is derived and approximated using an additional OLA for steady state conditions.Novel update laws for tuning the unknown parameters of the OLAs online are derived.Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded error.In the absence of OLA reconstruction errors,an optimal control is demonstrated.Simulation results verify that all OLA parameter estimates remain bounded,and the proposed OLA-based optimal control scheme tunes itself to reduce the cost HJB equation.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

A Contractive Sliding-mode MPC Algorithm for Nonlinear Discrete-time Systems

This paper investigates a sliding-mode model predictive control （MPC） algorithm with auxiliary contractive sliding vector constraint for constrained nonlinear discrete-time systems. By adding contractive constraint into the optimization problem in regular sliding-mode MPC algorithm, the value of the sliding vector is decreased to zero asymptotically, which means that the system state is driven into a vicinity of sliding surface with a certain width. Then, the system state moves along the sliding surface to the equilibrium point within the vicinity. By applying the proposed algorithm, the stability of the closed-loop system is guaranteed. A numerical example of a continuous stirred tank reactor （CSTR） system is given to verify the feasibility and effectiveness of the proposed method.

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.

Stabilization of Unknown Nonlinear Discrete-Time Delay Systems Based on Neural Network

This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity. Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities. Finally, a relevant example is given to illustrate the effectiveness of the proposed control scheme.

A novel extended Tsypkin criterion for discrete-time descriptor systems with ferromagnetic hysteresis nonlinear physical phenomenon

This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.

A New Uniformly Ultimate Boundedness Criterion for Discrete-Time Nonlinear Systems

A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assumed to be positive definite and its difference at the every latter moment and the former moment is negative definite. In this paper the condition of difference of Lyapunov function is relaxed. Under the relaxed condition, the result of this paper can be considered as the extension of the classical Lyapunov theory about uniformly ultimate boundedness.

DECOMPOSITION OF NONLINEAR DISCRETE-TIME STOCHASTIC SYSTEMS

This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.

Dual-stage Optimal Iterative Learning Control for Nonlinear Non-affine Discrete-time Systems

根据沿着重复轴的一种新动态 linearization 技术，双阶段的最佳的反复的学习控制为非线性、非仿射的分离时间的系统被介绍。双阶段显示二个最佳的学习阶段分别地被设计反复地改进控制输入顺序和学习获得。主要特征是控制器设计和集中分析仅仅取决于动态系统的 I/O 数据。换句话说，没有知道系统的任何另外的知识，我们能容易选择控制参数。模拟学习沿着重复轴说明介绍方法的几何集中，在哪个马路的一个例子控制为它的内在的工程重要性是引人注目的交通反复的学习。

Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems

In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.

Robust Sliding-mode Filtering for a Class of Uncertain Nonlinear Discrete-time State-delayed Systems

This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.