一类不确定模糊模型的输出反馈鲁棒预测控制

针对一类满足扇形界条件的不确定模糊模型描述的非线性系统,提出一种输出反馈鲁棒预测控制方法．该方法将鲁棒预测控制的Min-Max优化问题转化为具有LMI约束的线性目标最小化问题,并且不需系统状态完全可测,仅仅利用系统测量输出和不可测状态的界限值来确定保证闭环系统鲁棒稳定的输出反馈控制器．仿真实验证明了该方法的有效性．     

Fuzzy observer design using linear matrix inequalities for fuzzy closed-loop control systems

Linear observers play an important role in modern control theory and practice. A systematic design method of fuzzy observers would be important for fuzzy control as well. The fuzzy observer is designed by solving linear matrix inequalities (LMI) that represent control performance such as disturbance rejection and robust stability. Our approach in designing the fuzzy observer is based on the LMI formulation of the stability conditions for closed-loop Takagi-Sugeno (T-S) fuzzy systems, when states are not available for measurement of feedback. We present a new approach, which is to design an observer based on fuzzy implications, with fuzzy sets in the antecedents, and an asymptotic observer in the consequents. Each fuzzy rule is responsible for observing the states of a locally linear subsystem. An example illustrates the design procedure.     

基于矩阵测度的非线性广义时滞系统鲁棒模糊控制

研究T-S模糊广义时滞系统的鲁棒控制问题.不同于传统的寻求公共正定矩阵的方法,基于矩阵测度给出保证系统鲁棒稳定的充分条件,并将此条件进一步转化为线性矩阵不等式.通过求解线性矩阵不等式,得到状态反馈控制器和静态输出反馈控制器.最后通过算例仿真验证了方法的有效性.     

An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model

This study presents a fuzzy model-based control criterion for time-delay chaotic systems with uncertainty. The Takagi-Sugeno (T-S) fuzzy model is adopted for representing a chaotic system possessing a time delay. A unified approach for designing a fuzzy observer, which integrates parallel distributed compensation with an adaptive updating method, is first discussed. An observer-based fuzzy control scheme is then developed to deal with stabilization and tracking problems. Based on Lyapunov stability analysis, sufficient conditions that ensure robust control performance of time-delay chaotic systems are derived. These conditions are represented in terms of linear matrix inequalities and adaptive updating laws. Finally, the proposed approach is validated through numerical synchronization, stabilization, and model tracking control simulations.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

基于模糊模型的非线性不确定时滞系统的H-infinite鲁棒容错控制

研究了一类具有不确定时滞的非线性系统的H_∞鲁棒容错控制问题. 采用T-S模糊模型来描述非线性系统,并对执行器失效且具有扰动的情形, 基于Lyapunov稳定性理论和LMI方法, 给出了系统H_∞鲁棒容错控制器存在的充分条件, 保证了系统的鲁棒稳定性. 仿真实例验证了本文提出方法的有效性.     

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.     

基于LMI的不确定离散模糊时滞系统鲁棒控制

利用T-S模糊模型,讨论了一类具有状态时滞和控制输入时滞的不确定离散非线性系统鲁棒控制问题,基于Lyapunov稳定性理论,导出了系统采用线性矩阵不等式表示的时滞相关型鲁棒镇定充分条件,并设计了相应的状态反馈模糊控制器．仿真结果证明了所提出方法的有效性和可行性.     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.     

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.     

一类不确定模糊系统的二次稳定性的研究

利用T-S模糊模型对一类非线性连续不确定时滞系统进行建模,通过对时变时滞不确定T-S模糊系统基于状态反馈控制器二次稳定性问题的分析,给出了使系统二次稳定具有增益变化的模糊状态反馈控制器存在的充分条件,该充分条件以线性矩阵不等式的形式给出,因其所有参数都是线性的,所以具有数值易解性.设计实例表明了该设计方法的可行性和有效性.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems

This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H^infin control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all epsivisin(0,epsiv^*) and the allowable perturbation bound epsiv^* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme     

基于观测器的参数不确定非线性系统的模糊鲁棒控制

对一类非线性系统进行模糊建模及其模糊观测器设计，研究了在系统的状态不可测且存在参数不确定的模糊鲁捧控制问题，以线性矩阵不等式的形式给出了模糊控制系统具有李雅普诺夫意义下稳定的充分条件，最后把所提出的方法应用到倒立摆系统进行仿真，仿真结果验证了该控制方法的有效性。     

基于观测器的参数不确定非线性系统的模糊鲁棒控制

对一类非线性系统进行模糊建模及其模糊观测器设计, 研究了在系统的状态不可测且存在参数不确定的模糊鲁棒控制问题, 以线性矩阵不等式的形式给出了模糊控制系统具有李雅普诺夫意义下稳定的充分条件, 最后把所提出的方法应用到倒立摆系统进行仿真, 仿真结果验证了该控制方法的有效性.     

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.     

Robust fuzzy tracking control for nonlinear networked control systems with integral quadratic constraints

This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying network-induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC). Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.     

一类不确定多输入模糊双线性系统的鲁棒H∞控制

针对一类带有参数不确定性和干扰的多输入模糊双线性系统(FBS)的鲁棒H_∞控制问题,使用并行分布补偿算法(PDC)设计了模糊控制器,得到了整个模糊控制系统鲁棒全局稳定的充分条件,控制器的设计可以通过求解一系列线性矩阵不等式(LMI)获得.仿真例子验证了方法的有效性.     

Stability analysis and design of Takagi-Sugeno fuzzy systems

This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach.