改进的T-S 模糊模型鲁棒稳定条件及其在转台控制中的应用

提出了参数不确定T-S 模糊系统的新型鲁棒镇定条件．该条件表示为线性矩阵不等式（LMI）的形式, 将模糊子系统的相互关系收集到一系列矩阵而不是单个矩阵中,因此比近期刊出文献中的宽松二次镇定条件具有更 小的保守性．以该LMI 条件为基础,容易得到不确定T-S 模糊控制系统的状态反馈鲁棒镇定控制器．由于只涉及一 组LMI,控制器设计简单并易于数值求解．在转台这一具有参数不确定性的连续时间非线性系统的控制中,所提方 法的有效性得到成功验证．     

基于观测器的非线性不确定离散系统的鲁棒模糊控制

研究了参数不确定及状态变量难以获取的非线性系统的鲁棒模糊控制问题.采用离散模糊T-S模型对离散非线性系统进行建模并建立了模糊观测器.用矩阵不等式的形式推导出了在Lyapunov意义下鲁棒镇定的充分条件.利用线性矩阵不等式(LMI)导出了模糊反馈增益和模糊观测器增益存在的充分条件.     

一类不确定非线性时滞系统的鲁棒H∞控制

针对一类状态和状态时滞具有不确定性的时滞系统,研究了该系统基于T-S模糊模型的鲁棒H∞控制器的设计问题。采用线性矩阵不等式LMI的方法,设计一个包含状态变量导数的模糊控制器,得到了系统鲁棒镇定且满足H∞性能指标的充分条件,此充分条件等价于一类线性矩阵不等式的可解性,通过仿真说明了控制器的有效性。     

一类模糊时滞系统指定衰减度的鲁棒控制

研究了一类非线性时滞系统基于模糊T-S模型的鲁棒镇定问题,所考虑的不确定时滞系统含有时变未知但有界的状态时滞,首先利用Razumikhin定理和Lyapunov定理,得出了由模糊T-S模型描述的非线性时滞系统鲁棒稳定且具有指定衰减度的判据,其次得到了具有指定衰减度的无记忆状态反馈控制律存在的充分条件及相应的控制器设计方法,该条件被进一步等价地转化为一个线性矩阵不等式的可解性问题,所设计的控制器确保了闭环系统具有指定衰减度鲁棒稳定。     

不确定多时滞离散切换系统的输出反馈镇定

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统,研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题.首先通过状态变量的替换将多时滞项转变成不含时滞项,再利用分段Lyapunov函数和线性矩阵不等式方法,导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件,并将此条件转化成为一组线性矩阵不等式的可行性问题,同时给出基于状态观测器的输出反馈控制器.仿真结果表明设计方法是可行有效的.     

考虑随机时滞的非线性网控系统鲁棒L2-L∞控制

本文考虑了由Takagi-Sugeno(T-S)模糊模型描述的一类连续非线性网络控制系统基于观测器的鲁棒L_2–L_∞控制器设计问题.假设网络环境下存在的时变时滞具有特定的随机特性,通过引入一个伯努利随机变量表示时滞在不同区间上分布的概率,建立一个新的具有概率分布信息的系统模型.根据平行分布补偿法(parallel distribution compensation,PDC)和Lyapunov稳定性理论,建立基于T-S模糊模型的使系统均方指数稳定且满足L_2–L_∞的性能判据.并利用线性矩阵不等式(linear matrix inequality,LMI)技术同时得到状态观测器增益矩阵和控制器增益矩阵.最后,仿真结果验证了该方法的有效性.     

基于T-S模糊模型的转台鲁棒最优控制器设计

针对飞行器仿真转台系统的非线性以及不确定性问题,提出了基于T-S模糊模型的鲁棒最优控制器设计方法.首先,利用IF-THEN模糊规则将转台速度环系统的状态空间分成不同的区域,构建具有参数不确定性的T-S模糊模型;然后,根据给定的最优性能指标要求以及控制输入约束,通过求解一组线性矩阵不等式(LMIs)进行鲁棒最优控制嚣设计.仿真结果表明,该方法不仅具有比较好的控制效果,而且能有效地解决控制输入约束问题,并能很好地保证对参数变化的鲁棒稳定性.     

鲁棒极点配置约束下的模糊控制系统设计

针对一类利用T-S模糊模型近似描述的不确定非线性系统,给出了一种具有鲁棒极点配置功能的模糊控制器和模糊状态观测器的设计方法.首先,利用并行分配补偿(PDC)设计思想和基于线性矩阵不等式(LMI)的鲁棒极点配置理论,得到了使整个闭环系统全局渐近稳定并满足希望的动态性能的充分条件.然后将这些条件转化为标准的LMI问题.最后将该设计方法应用于倒立摆的平衡控制中,验证了本方法的有效性.     

基于观测器的时滞系统鲁棒控制器的设计

研究了一类不确定时滞系统基于观测器的鲁棒镇定问题,系统的不确定性时变未知且范数有界,目的是设计状态观测器和线性无记忆观测状态反馈控制器,使其能够镇定一类状态和控制输入不确定性时滞系统。基于Lyapunov稳定性理论,采用线形矩阵不等式这一有效工具,给出了系统基于观测状态反馈鲁棒镇定的充分条件,并且利用线形矩阵不等式的解构造了使得系统鲁棒稳定的基于观测状态反馈控制器,所得结果与时滞相关,从而相对减弱了控制器设计的保守性。数值算例表明了所提出的设计方法的有效性。     

不确定非线性时滞系统的广义H_2控制

对连续时间非线性系统的广义H2控制问题进行了研究。针对系统具有时变状态时滞和范数有界不确定性的特点,基于T-S模型,采用Lyapunov函数和线性矩阵不等式方法,得出此类非线性系统存在鲁棒H2模糊控制器的充分条件。该条件等价于两类线性矩阵不等式的可解性。仿真结果验证了算法的有效性。     

Robust fuzzy control of nonlinear systems with parametricuncertainties

Addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model is adopted for fuzzy modeling of the nonlinear system. Two cases of the T-S fuzzy system with parametric uncertainties, both continuous-time and discrete-time cases are considered. In both continuous-time and discrete-time cases, sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic Lorenz system     

T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems

This paper proposes a fuzzy bilinear model for a class of nonlinear systems and a fuzzy controller to stabilize such systems. By examination of a modeling problem, we describe how to transform a nonlinear system into a bilinear one via Taylor's series expansion and then we adopt the Takagi-Sugeno (T-S) fuzzy modeling technique to construct a fuzzy bilinear model. For controller design, the parallel distributed compensation (PDC) method is utilized to stabilize the fuzzy bilinear system (FBS), and some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Moreover, we propound some sufficient conditions for robust stabilization of the FBS with parametric uncertainties. Finally, a numerical example and the Van de Vusse model are utilized to demonstrate the validity and effectiveness of the proposed FBS.     

Robust PI controller design for nonlinear systems via fuzzymodeling approach

The design problem of proportional and proportional-plus-integral (PI) controllers for nonlinear systems is studied. First, the Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties is used to approximate the nonlinear systems. Then a numerically tractable algorithm based on the technique of iterative linear matrix inequalities is developed to design a proportional (static output feedback) controller for the robust stabilization of the system in T-S fuzzy model. Next, we transform the problem of PI controller design to that of proportional controller design for an augmented system and thus bring the solution of the former problem into the configuration of the developed algorithm. Finally, the proposed method is applied to the design of robust stabilizing controllers for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy PI controller when large faults appear in the system, compared to the conventional PI controller designed by using linearization method around the steady state     

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.     

Robust sampled-data fuzzy control of nonlinear systems with parametric uncertainties: Its application to depth control of autonomous underwater vehicles

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi-Sugeno (T-S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.     

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     

Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.     

一类不确定时滞模糊系统的鲁棒H∞控制

对于一类不确定非线性时滞系统,研究使系统二次稳定的状态反馈控制方法。利用T—S模糊模型对时变时滞不确定非线性系统进行建模,采取分段光滑（PSQ）的Lyapunov函数和线性矩阵不等式方法给出使系统二次稳定的模糊状态反馈控制器存在的充分条件,避免并行补偿法中求解公共矩阵P的困难。仿真试验证明,通过该方法设计的控制器具有良好的鲁棒性,控制效果良好。     

A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems

This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature. A rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases. In comparison with conventional conditions, the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design. The latter design work is quite hard for T-S fuzzy control systems. Based on the LMI-based conditions derived, one can easily synthesize controllers for stabilizing T-S fuzzy control systems. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.