基于观测器的不确定广义时滞系统保成本控制

讨论了基于观测器的一类不确定广义时滞系统的保成本控制问题,给出了系统保成本控制器的设计方法.控制器的构造使得闭环系统是鲁棒稳定的.利用线性矩阵不等式以及Lyapunov函数方法,给出了鲁棒保成本控制器存在的充分条件以及相应的可保成本指标,并证明了这个条件等价于一组线性矩阵不等式(LM Is)的可解性问题,同时推广了已知的相关结果.最后以算例验证了设计方法的有效性.     

基于T-S模型的非线性时滞系统非脆弱保性能模糊控制

针对一类用T-S模糊模型描述的非线性时滞系统,采用状态反馈的并行分布补偿方法,研究其保守性较小的非脆弱保性能模糊控制问题,使闭环系统在控制器存在加性摄动的情况下,其闭环性能指标值低于确定的上界.利用线性矩阵不等式处理方法,导出了非脆弱保性能模糊控制律的存在条件,通过建立和求解一个线性矩阵不等式问题,给出了非脆弱保性能模糊控制律的设计方法.仿真结果表明了所提出方法的有效性.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays

This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

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.     

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。     

参数不确定T-S模糊交联系统的分散保成本控制

研究了参数不确定T-S模糊交联系统的分散保成本控制问题.对于给定系统所容许的所有不确定参数,设计了分散状态反馈保成本控制器,使得闭环系统不仅渐近稳定而且具有适当的性能指标上界.基于线性矩阵不等式(LM I)处理方法,给出了分散控制器存在的充分条件.仿真算例表明了所给方法的简易、有效.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Guaranteed Cost Control for Discrete-time Singular Large-scale Systems with Parameter Uncertainty

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper.The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model.The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncer- tainties.A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities(LMIs),and a desired state feedback controller is obtained via con- vex optimization.An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

一类关联不确定离散系统的分散保性能控制

结合一个给定的二次型性能指标, 研究一类关联不确定离散大系统的分散保性能状态反馈控制器设计问题. 采用线性矩阵不等式处理方法, 导出了分散控制器存在的条件, 并给出了一组分散保性能控制器的参数化表示, 据此, 通过建立和求解一个凸优化问题给出了使得闭环性能指标的上界最小化的最优分散保性能控制器设计方法.     

Guaranteed cost repetitive control for uncertain discrete-time systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method for the repetitive control systems by introducing a robust output feedback controller so that the closed-loop system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. Necessary and sufficient conditions for the existence of such controllers are derived in terms of linear matrix inequality (LMI). A suboptimal guaranteed cost controller is obtained by solving an optimization problem with LMI constraints. Finally, a simulation example is provided to illustrate the validity of the proposed method.     

一类不确定模糊动态时滞系统保成本控制

针对一类不确定非线性动态时滞系统，利用模相T—S模型，通过状态反馈对保成本控制问题进行研究。应用线性矩阵不等式给出模糊闭环系统渐近稳定的充分条件，保证了所有允许的不确定闭环系统是稳定的，而且对于一个给定的二次型成本函数，舱保证闭环成本不超过某个界。仿真结果表明所提出的控制方法是有效的。     

Intelligent digital redesign for nonlinear systems using a guaranteed cost control method

In this paper, a novel intelligent digital redesign (IDR) technique using the guaranteed cost control method is proposed for nonlinear systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique, which is one of the sampled-data fuzzy controller design methods, guarantees not only the stability condition of the sampled-data closed-loop system with the sampleddata fuzzy controller and the state-matching error is presented. By using the concept of the guaranteed cost control method, sufficient conditions are obtained for both minimization of the state-matching error and stabilization of the sampled-data closed-loop system and derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.     

A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties

This paper investigates the problem of guaranteed cost control for Takagi-Sugeno fuzzy dynamic systems with interval parameter uncertainties. The parameter uncertainty is characterized by the matrix bound, which is quite natural in real applications. Attention is focused on the fuzzy state feedback controller design via the so-called parallel distributed compensation scheme, which guarantees the closed-loop system to be robustly stable with a prescribed upper bound of the cost function. By utilizing the instrumental idea of delay dividing, a new Lyapunov-Krasovskii functional is introduced, which leads the resultant conditions to be much less conservative than most existing results in the literature. Some other new ideas such as basis dependence are also employed, which help to reduce the conservatism. All the results are formulated in the form of linear matrix inequalities (LMIs), which can readily be solved via standard numerical software. Finally, illustrative examples are given to show the less conservatism and applicability of the obtained results.     

Guaranteed cost control for T-S fuzzy systems with time-varying delays

This paper deals with the problem of guaranteed cost control for nonlinear systems with time-varying delays which is represented by Takagi-Sugeno (T-S) fuzzy models with time-varying delays. The derivatives of timevarying delay are not necessary to be bounded. Based on the free weighting matrix method, sufficient conditions for the existence of fuzzy guaranteed cost controller via state feedback are given in terms of linear matrix inequalities (LMIs). A minimizing method is also proposed to search the suboptimal upper bound of the guaranteed cost function. The results are delay-dependent but contain delay-independent criteria as a special case. A numerical example is presented to demonstrate the effectiveness and less conservativeness of our work.     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.