Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities(LMIs).     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

This article is concerned with the consensus problem for discrete‐time multiagent systems with both state and input delays. Single observer‐predictor‐based protocols and multiple observer‐predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer‐predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer‐error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Adaptive Decentralized NN Control of Nonlinear Interconnected Time‐Delay Systems with Input Saturation

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large‐scale uncertain nonlinear time‐delay systems with input saturation. Radial basis function (RBF) neural networks (NNs) are used to tackle unknown nonlinear functions. Then, the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique, along with the minimal‐learning‐parameters (MLP) algorithm. The stability analysis subject to the effect of input saturation constraints are conducted with the help of an auxiliary design system based on the Lyapunov–Krasovskii method. The proposed controller guarantees uniform ultimate boundedness (UUB) of all of the signals in the closed‐loop large‐scale system, while the tracking errors converge to a small neighborhood around the origin. An advantage of the proposed control scheme lies in the number of adaptive parameters of the whole system being reduced to one and in the solution of the three problems of “computational explosion,” “dimension curse,” and “controller singularity”. Finally, simulation results along with comparisons are presented to demonstrate the advantages, effectiveness, and performance of the proposed scheme.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Adaptive fuzzy semi‐decentralized control for a class of large‐scale nonlinear systems with unknown interconnections

In this paper, a general method is developed to generate a stable adaptive fuzzy semi‐decentralized control for a class of large‐scale interconnected nonlinear systems with unknown nonlinear subsystems and unknown nonlinear interconnections. In the developed control algorithms, fuzzy logic systems, using fuzzy basis functions (FBF), are employed to approximate the unknown subsystems and interconnection functions without imposing any constraints or assumptions about the interconnections. The proposed controller consists of primary and auxiliary parts, where both direct and indirect adaptive approaches for the primary control part are aiming to maintain the closed‐loop stability, whereas the auxiliary control part is designed to attenuate the fuzzy approximation errors. By using Lyapunov stability method, the proposed semi‐decentralized adaptive fuzzy control system is proved to be globally stable, with converging tracking errors to a desired performance. Simulation examples are presented to illustrate the effectiveness of the proposed controller. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust Adaptive Neural Network Control For A Class Of Multiple‐Input Multiple‐Output Nonlinear Time Delay System With Hysteresis Inputs And Dynamic Uncertainties

This paper studies an adaptive neural control for nonlinear multiple‐input multiple‐output systems with dynamic uncertainties, hysteresis input, and time delay. The studied systems are composed of N nonlinear time‐delay subsystems and the interconnection terms are contained in every equation of each subsystem. Adaptive neural control algorithms are developed by introducing a well‐defined smooth function. The unknown time‐varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing an available dynamic signal. The main advantage of the proposed controllers is that they contain fewer parameter estimates that need to be updated online. Consequently, the accuracy of ultimate tracking errors asymptotically approaches a pre‐defined bound, and all signals in the closed‐loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed adaptive neural network control schemes.     

采用还原方法的不确定关联时滞系统的鲁棒分散镇定

针对一类具有多输入时滞项及互联时滞项的不确定关联系统，提出了系统可鲁棒分散镇定的充分条件，即一组线性矩阵不等式(LMI)有解．系统的不确定性是未知时变且范数有界的，基于还原方法及LMI技术给出系统设计状态反馈分散控制器的方法．该控制器保证闭环系统全局渐近稳定，且设计简单，计算量小，易于工程实现．最后通过仿真例子说明了该方法的有效性．     

变时滞不确定组合系统基于观测器的鲁棒镇定

研究一类孤立子系统中状态及控制输入均含有时变时滞,且互联项也含有时变时滞的不确定组合系统基于状态观测器的鲁棒控制问题.基于一组线性矩阵不等式（LMIs）解的存在性,并依据Razumikhin-type理论和Lyapunov稳定性理论,给出了保证系统可鲁棒分散镇定的充分条件及相应控制器的设计方法.分散控制器可通过求解一组LMIs得到.最后,利用一个数值例子验证了所给设计方法的有效性.     

线性滞后互联大系统的分散智能镇定

讨论了线性滞后互联大系统的分散镇定问题,给出了分散镇定控制器设计的思想 和方法,而后将人工神经网络技术引入该研究领域,给出了一般线性定常系统闭环极点配置 的智能方法,同时实现了线性滞后互联大系统分散镇定控制器的智能设计.最后给出了一数 值仿真例子,进而验证了该设计方法的可行性及有效性.     

Input-to-state stability analysis for interconnected difference equations with delay

Input-to-state stability (ISS) of interconnected systems with each subsystem described by a difference equation subject to an external disturbance is considered. Furthermore, special attention is given to time delay, which gives rise to two relevant problems: (i) ISS of interconnected systems with interconnection delays, which arise in the paths connecting the subsystems, and (ii) ISS of interconnected systems with local delays, which arise in the dynamics of the subsystems. The fact that a difference equation with delay is equivalent to an interconnected system without delay is the crux of the proposed framework. Based on this fact and small-gain arguments, it is demonstrated that interconnection delays do not affect the stability of an interconnected system if a delay-independent small-gain condition holds. Furthermore, also using small-gain arguments, ISS for interconnected systems with local delays is established via the Razumikhin method as well as the Krasovskii approach. A combination of the results for interconnected systems with interconnection delays and local delays, respectively, provides a framework for ISS analysis of general interconnected systems with delay. Thus, a scalable ISS analysis method is obtained for large-scale interconnections of difference equations with delay.     

Interconnected jumping time‐delay systems: Mode‐dependent decentralized stability and stabilization

In this paper, we deal with the problems of mode‐dependent decentralized stability and stabilization with ??_∞ performance for a class of continuous‐time interconnected jumping time‐delay systems. The jumping parameters are governed by a finite state Markov process and the delays are unknown time‐varying and mode‐dependent within interval. The interactions among subsystems satisfy quadratic bounding constraints. To characterize mode‐dependent local stability behavior, we employ an improved Lyapunov–Krasovskii functional at the subsystem level and express the stability conditions in terms of linear matrix inequalities (LMIs). A class of local decentralized state‐feedback controllers is developed to render the closed‐loop interconnected jumping system stochastically stable. Then, we extend the feedback strategy to dynamic observer‐based control and establish the stochastic stabilization via LMIs. It has been established that the developed results encompass several existing results as special cases which are illustrated by simulation of examples. Copyright © 2011 John Wiley & Sons, Ltd.     

基于嵌套?伪预估器反馈的时滞控制系统输入时滞补偿

本文研究同时具有输入和状态时滞的控制系统的输入时滞补偿问题. 通过建立嵌套?伪预估器反馈方法预测系统未来的状态, 使得任意大但有界的输入时滞得到完全补偿. 不同于传统的预估器反馈利用开环系统预测系统未来的状态, 嵌套?伪预估器反馈则是利用闭环系统嵌套地预测系统未来的状态. 依据积分时滞系统的稳定性, 给出了保证闭环系统渐近稳定的充要条件. 最后, 采用数值仿真验证所提出方法的有效性.     

Parametric Absolute Stabilization for Interconnected Lurie Time‐Delay Systems with Polytopic Uncertainty

The paper considers the parametric absolute stabilization for interconnected Lurie time‐delay systems with polytopic uncertainty. The concept of parametric absolute stabilization characterizes both the existence and the stability of equilibrium in the case of uncertain parameters and reference input shift. First, the existing conditions of parametric stability and the stable region are studied by the change of the uncertain parameters and reference input based on decentralized state feedback. Then, a delay‐dependent absolute stability condition in parametric stabilization region for interconnected Lurie time‐delay systems with polytopic uncertainties is obtained through a linear matrix inequality method. Finally, an example is given to illustrate the effectiveness of the proposed method.     

基于分散反馈控制的时滞混沌大系统

研究一类具有时滞关联的时滞大系统的混沌现象和分散反馈控制问题。应用线性矩阵不等式（LMI）方法,基于李雅普诺夫定理,分别得到了系统存在分散时滞反馈控制器和分散标准反馈控制器的充分条件,并利用分散时滞反馈控制器对系统中存在的不稳定周期轨道的追踪控制问题进行研究。仿真结果表明控制器具有很强的鲁棒性。     

线性连续时滞大系统的分散镇定控制

针对线性连续时滞大系统,建立了在一定关联矩阵分解情形下的镇定条件,同时,给出了分散局部无记忆状态反顺的设计方法,最后,给出一个示例说明所得方法并比较文献中已有结果。