H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

This paper presents a design method of H₂ guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H₂ GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H₂ performance index. Furthermore, an optimal H₂ GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.     

基于观测器的不确定T-S模糊系统鲁棒镇定

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件. 该条件用来设计模糊控制器和模糊观测器. 为了设计模糊控制器和模糊观测器, 用T-S模糊模型来表示非线性系统, 并运用平行分布补偿观念. 充分条件基于二次Lyapunov函数, 通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式, 比以往文献中列出的条件具有更小的保守性. 该不等式为双线性矩阵不等式, 可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益. 最后, 通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.     

Robust H2 guaranteed cost fuzzy control for uncertain discrete‐time fuzzy systems via poly‐quadratic Lyapunov functions

In this paper, new approaches regarding H₂ guaranteed cost stability analysis and controller synthesis problems for a class of discrete‐time fuzzy systems with uncertainties are investigated. The state‐space Takagi‐Sugeno fuzzy model with norm‐bounded parameter uncertainties is adopted. Based on poly‐quadratic Lyapunov functions, sufficient conditions for the existence of the robust H₂ fuzzy controller can be obtained in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design a suboptimal fuzzy controller which minimizes the upper bound on the quadratic cost function. The effectiveness of the proposed design approach is illustrated by two examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems

This paper presents a novel observer-based hybrid adaptive fuzzy controller for affine and nonaffine nonlinear systems with external disturbance. The suggested design is so easy and does not need a mathematical model for system under control and also it is very simple, efficient and robust. Based on the adaptive method and the system states observer, an observer-based adaptive fuzzy method is proposed to control an uncertain nonlinear system. Also, a supervisory controller term is employed to attenuate the residual error to a desired level and compensate the both uncertainties and observer errors. Although proposed control method needs the uncertainties to be bounded, it does not need this bound to be identified. Stability of the proposed method is shown based on Lyapunov theory and also the strictly positive real condition if all the implicated signals are uniformly bounded. Finally, in our simulation studies, to demonstrate the usefulness and efficiency of the suggested technique, an uncertain nonlinear system is employed.

     

Observer-based H∞ controller for 2-D T–S fuzzy model

This paper develops a method of fuzzy observer-based H_∞ controller design for two-dimensional (2-D) discrete Takagi–Sugeno (T–S) fuzzy systems. By reformulating the system, a linear matrix inequality (LMI)-based sufficient condition is derived. Then the fuzzy controller and the fuzzy observer can be independently designed, which guarantee an H_∞ noise attenuation γ of the whole system. Owing to the introduction of free matrices, the presented design method has a wider range of application and can guarantee a better H_∞ performance of the closed-loop fuzzy control system. Simulation results have demonstrated the effectiveness of the proposed method.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Non-fragile guaranteed cost fuzzy control for nonlinear first-order hyperbolic partial differential equation systems

This paper concerns the non-fragile guaranteed cost control for nonlinear first-order hyperbolic partial differential equations (PDEs), and the case of hyperbolic PDE systems with parameter uncertainties is also addressed. A Takagi–Sugeno (T–S) fuzzy hyperbolic PDE model is presented to exactly represent the nonlinear hyperbolic PDE system. Then, the state-feedback non-fragile controller distributed in space is designed by the parallel distributed compensation (PDC) method, and some sufficient conditions are derived in terms of spatial differential linear matrix inequalities (SDLMIs) such that the T–S fuzzy hyperbolic PDE system is asymptotically stable and the cost function keeps an upper bound. Moreover, for the nonlinear hyperbolic PDE system with parameter uncertainties, using the above-design approach, the robust non-fragile guaranteed cost control scheme is obtained. Furthermore, the finite-difference method is employed to solve the SDLMIs. Finally, a nonlinear hyperbolic PDE system is presented to illustrate the effectiveness and advantage of the developed design methodology.     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.     

Observer-based <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> guaranteed cost control for uncertain singular time-delay systems with input saturation

In this paper, the problem of observer-based H _∞ guaranteed cost control for uncertain singular timedelay systems with actuator saturation is concerned. A delay-dependent sufficient condition is proposed, which guarantees that the closed-loop system is admissible via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region, the upper bound of cost function and the design method of observer-based H _∞ guaranteed cost controller are given by solving linear matrix inequalities and convex optimization problems. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

一类不确定离散非线性时滞系统保性能控制

针对状态不完全可测的一类不确定连续离散时间非线性系统,基于状态观测器研究其保性能控制问题。采用T-S模型对非线性系统进行建模,根据李雅普诺夫稳定性理论,基于线性矩阵不等式(LMI),利用分散化并行分布补偿(PDC)的方法设计了基于观测器的控制器,给出了实现该非线性系统保性能控制的充分条件。在此基础上通过求解相应的线性矩阵不等式组给出了控制器和观测器的设计方法,并通过数值仿真验证了提出的方法,仿真结果表明该方法是正确的。     

基于观测器的滑模控制非线性中立型时滞系统

针对一类状态不可测的非线性不确定中立型时滞系统,基于滑模控制理论,采用线性矩阵不等式的处理方法,提出了滑动模态鲁棒渐近稳定时滞相关的充分条件,设计了一类滑模观测器,同时给出了该观测器存在的充分条件;然后应用滑模控制的趋近率方法和基于观测器所得到的系统估计状态,综合了一类滑模控制器,该控制器同时保证了估计状态下滑模面和估计误差状态下滑模面的渐近可达性;最后通过数值实例证明了该控制方案的可行性.     

Robust H∞ control for Van de Vusse reactor via T–S fuzzy bilinear scheme

This paper proposes a fuzzy bilinear scheme including a fuzzy modeling method and a fuzzy controller for a class of uncertain nonlinear systems with an additive disturbance input. Firstly, this procedure of modeling describes how to transform a nonlinear system into a fuzzy bilinear system (FBS). For controller design problem, the parallel distributed compensation (PDC) method is adopted to design a fuzzy controller which ensures the robust asymptotic stability of the uncertain T–S FBS with an additive disturbance input and guarantees an H_∞ norm bound constraint on disturbance attenuation. Besides, some sufficient conditions are derived to guarantee the robust stabilization of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, the Van de Vusse reactor (Chen, Lin, Lin, & Tong, 2008; Chong & Zak, 1996; Kashiwagi & Rong, 2002; Li, Tsai, Lee, Hsiao, & Chao, 2008; Perez, Ogunnaike, & Devasia, 2000) with additive disturbance input is utilized to demonstrate the validity and feasibility of the proposed control scheme.     

Robust H∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.     

A new robust observer-based adaptive type-2 fuzzy control for a class of nonlinear systems

In this paper, a novel robust observer-based adaptive controller is presented using a proposed simplified type-2 fuzzy neural network (ST2FNN) and a new three dimensional type-2 membership function is presented. Proposed controller can be applied to the control of high-order nonlinear systems and adaptation of the consequent parameters and stability analysis are carried out using Lyapunov theorem. Moreover, a new adaptive compensator is presented to eliminate the effect of the external disturbance, unknown nonlinear functions approximation errors and sate estimation errors. In the proposed scheme, using the Lyapunov and Barbalat's theorem it is shown that the system is stable and the tracking error of the system converges to zero asymptotically. The proposed method is simulated on a flexible joint robot, two-link robot manipulator and inverted double pendulums system. Simulation results confirm that in contrast to other robust techniques, our proposed method is simple, give better performance in the presence of noise, external disturbance and uncertainties, and has less computational cost.     

Robust H ∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H _∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H _∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H _∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.     

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.     

Interval type 2 hierarchical FNN with the H-infinity condition for MIMO non-affine systems

To develop a controller that deals with noise-corrupted training data and rule uncertainties for interconnected multi-input–multi-output (MIMO) non-affine nonlinear systems with unmeasured states, an interval type-2 fuzzy system is integrated with an observer-based hierarchical fuzzy neural controller (IT2HFNC) in this paper. Also, an H_∞ control technique and a strictly positive real Lyapunov (SPR-Lyapunov) design approach are employed for attenuating the influence of both external disturbances and fuzzy logic approximation error on the tracking of errors. Moreover, the proposed hierarchical fuzzy structure can greatly reduce the number of adjusted parameters of the IT2HFNC, and then, the problem of online computational burden can be solved. According to the design of the interval type-2 fuzzy neural network and H_∞ control technique, the IT2HFNN controller can improve its robustness to noise, uncertainties, approximation errors, and external disturbances. Simulation results are reported to show the performance of the proposed control system mode and algorithms.     

State-feedback stabilisation for fuzzy bilinear uncertain system with disturbance via fuzzy control approach

This article presents a fuzzy control scheme for a class of Takagi–Sugeno (T–S) fuzzy uncertain bilinear system with disturbance (FUBSD). First, the T–S FUBSD is established and based on the parallel distributed compensation method, the overall robust H _∞ fuzzy controller is proposed to globally stabilise the T–S FUBSD. Then, some sufficient conditions are derived to guarantee the robust stabilisability of the overall fuzzy control system via linear matrix inequalities. Finally, a numerical example is utilised to demonstrate the validity and effectiveness of the proposed control scheme.