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.

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control (ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis. © 2014 Chinese Association of Automation.

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

H_∞ Filter Design for Discrete-time Systems with Missing Measurements

For packet-based transmission of data over a network, or temporary sensor failure, etc., data samples may be missing in the measured signals. This paper deals with the problem of H∞ filter design for linear discrete-time systems with missing measurements. The missing measurements will happen at any sample time, and the probability of the occurrence of missing data is assumed to be known. The main purpose is to obtain both full-and reduced-order filters such that the filter error systems are exponentially mean-square stable and guarantee a prescribed H∞ performance in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed design approach.

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.

LMI Consensus Condition for Discrete-time Multi-agent Systems

This paper examines a consensus problem in multiagent discrete-time systems, where each agent can exchange information only from its neighbor agents. A decentralized protocol is designed for each agent to steer all agents to the same vector. The design condition is expressed in the form of a linear matrix inequality. Finally, a simulation example is presented and a comparison is made to demonstrate the effectiveness of the developed methodology.

Stability analysis and stabilization for discrete-time singular delay systems

Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems is derived.Then,by applying the skill of matrix theory,the state feedback controller is designed to guarantee the closed-loop discrete-time singular delay systems to be regular,casual and stable.Finally,numerical examples are given to demonstrate the effectiveness of the proposed method.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.

Feedback control design for discrete-time piecewise affine systems

This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine(PWA) systems.The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods.We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality(BMI) problem.Then,two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI.Several simulation examples are given to demonstrate the advantages of the proposed design.

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.

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.

Design of fuzzy sliding mode controller for SISO discrete-time systems

According to a class of nonlinear SISO discrete systems, the fiizzy sliding mode control problem is considered. Based on Takagi-Sugeno fuzzy model method, a fuzzy model is designed to describe the local dynamic performance of the given nonlinear systems. By using the sliding mode control approach, the global controller is constructed by integrating all the local state controllers and the global supervisory sliding mode controller. The tracking problem can be easily dealt with by taking advantage of the combined controller,and the robustness performance is improved finally. A simulation example is given to show the effectiveness and feasibility of the method proposed.

Stability Analysis of Discrete-time Systems with Additive Time-varying Delays

In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has practical application background in networked control systems . The stability criterion is expressed in the form of linear matrix inequalities （LMIs）, which can be readily solved by using standard numerical software. An illustrative example is provided to show the advantage of the proposed stability condition.