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.

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.

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.

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.

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.

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.

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.

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.

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.

Asymptotic controllability of a class of discrete-time systems with disturbances

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.

Stabilization of a class of nonlinear discrete time systems with time varying delay

The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.

A Discretization Method for Nonlinear Delayed Non-affine Systems

The input time delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. This paper proposes a new discretization method for calculating a sampled-data representation of nonlinear time-delayed non-affine systems. The proposed scheme provides a finite-dimensional representation for nonlinear systems with non-a^ne time-delayed input enabling existing nonlinear controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated by using a nonlinear system with non-affine time-delayed input. For this nonlinear system, various time delay values are considered.

Validity of Approach to Maximize the ASR of the Order Superiorly Two in Discrete Nonlinear Systems

This paper is, in fact, a proposal of a polynomial approach to the nonlinear systems control by using the concept of linearization by state feedback. In this context, a discretization method is presented. We developed a discrete control scheme based on an approximate feedback linearization method and the reversing trajectory method. The proposed control strategy sits on the methods of widening the stability domains of operating points. Such domains are expanded through the use of the non Lyapunov stability synthesis methods. Additionally, the developed technique is employed for the control of the class of systems with an order higher than two;more precisely, the example of a synchronous generator featured in a strongly nonlinear model.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

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.

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.

Fault detection for nonlinear discrete-time systems via deterministic learning

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions （i.e., the internal dynamics） underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function （RBF） networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.

Robust Neural Control of Discrete Time Uncertain Nonlinear Systems Using Sliding Mode Backpropagation Training Algorithm

This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.