具有控制约束的不确定离散时滞系统最优保性能控制

对一类具有范数有界时变参数不确定性和控制输入约束的离散时滞系统,研究其最优保性能状态反馈控制律的设计问题.基于线性矩阵不等式处理方法,导出了保性能控制律存在的条件,并证明了该条件等价于一组线性矩阵不等式的可行性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示.进而,通过建立并求解一个凸优化问题,给出了具有控制约束的最优保性能控制律设计方法.     

基于Delta算子的非线性系统最优模糊保性能控制

对一类Delta算子描述的具有范数有界不确定性的非线性T S模糊系统,研究其状态反馈最优保性能控制器设计问题。基于线性矩阵不等式(LMI)的方法,给出了存在和设计保性能控制律的一个充分条件。以及在使二次性能函数上界最小意义下,最优保性能控制律的凸优化设计方法。所得结果将连续和离散模糊系统的有关结论统一到Delta算子框架内。     

具有控制约束的不确定离散系统最优保性能控制

对一类具有范数有界时变参数不确定性和控制输入约束的离散时间线性系统,采用线性矩阵不等式处理方法,导出了保性能控制律存在的条件,证明了该条件等价于一组线性矩阵不等式的可行性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。进而,通过建立并求解一个凸优化问题,给出了具有控制约束的不确定离散系统最优保性能控制律设计方法。     

基于模糊双曲模型的非脆弱控制及其仿真研究

提出一种基于模糊双曲模型(FHM)的非脆弱保性能控制器设计方法.首先,用模糊双曲模型来表述一类离散非线性系统,建立基于模糊双曲模型的控制器.然后,同时考虑了加性和乘性两种形式的控制器增益摄动,利用Lyapunov方法和FHM的结构特点建立非脆弱保性能控制器的存在条件.其次,使用线性矩阵不等式(LMI)方法设计该控制器以保证闭环系统是渐近稳定的,并且可以通过求解一个基于LMl的优化问题,得到最优的控制器增益矩阵,同时使得保性能指标的上界最小.最后,通过仿真研究表明该方法的有效性.     

输入时滞Markov跳变系统鲁棒保性能控制及其仿真研究

研究一类具有模态相关时变输入和状态时滞的不确定马尔可夫跳变系统的鲁棒保性能控制问题。基于自由权矩阵方法,通过构造一个新的Lyapunov函数,给出了此类系统存在无记忆状态反馈鲁棒保性能控制律的充分条件,估计了其保性能值。并且,控制器的设计归结为一组LMI的求解问题。仿真实例说明了提出方法的有效性。     

不确定离散广义线性系统的保性能最优控制

对一类具有范数有界时不变参数不确定性的广义离散时间线性系统和一个二次型性能指标,研究了其最优保性能状态反馈控制律的设计问题。通过采用线性矩阵不等式方法,导出了存在保性能控制律的一个充分条件,进而证明了该条件可化为一个线性矩阵不等式的可解性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。在此基础上,通过建立并求解一个凸优化问题,给出了最优保性能控制律的设计方法,最后用例子说明了该方法的应用。     

不确定变时滞系统的模糊静态输出反馈保性能可靠控制

针对一类含有执行器故障的变时滞不确定性T-S模糊模型,采用静态输出反馈的并行分布补偿器(PDC)结构,研究了其模糊静态输出反馈保性能可靠控制律的设计问题。通过定义一类时滞相关Lyapunov-Kra-sovskii函数,基于线性矩阵不等式(LMI),给出了模糊静态输出反馈保性能可靠控制器存在的条件,所设计的控制器可保证在正常和执行器故障情况下,闭环系统都能渐近稳定,并且正常保性能上界小于故障保性能上界。仿真实验验证了该设计方法的有效性。     

跳变时滞随机系统的鲁棒保性能控制

研究了马尔可夫跳变参数时滞随机系统的鲁棒保性能控制问题。通过构造一个Lyapunov函数,并应用Ito微分公式沿系统对其求微分,再利用线性矩阵不等式(LMI)的性质和广义Ito公式,给出了此类系统保性能控制律存在的充分条件,估计了其保性能值,同时,控制器的设计归结为一族LMI的求解问题。最后,数值算例说明了方法的有效性。     

不确定广义系统的保成本可靠控制

对一类含有时变范数有界参数不确定广义系统和部分执行器可能失效的系统,结合一个二次型性能指标,研究了使得闭环系统保持正则、无脉冲和稳定,且闭环性能指标值不超过某个确定界的保成本可靠控制律的设计问题。通过矩阵不等式导出保成本可靠控制律的一个充分存在条件,进而用线性矩阵不等式给出了保成本可靠控制器的一个参数化的表示。在此基础上,通过建立并求解一个凸优化问题,给出了最优保成本可靠控制律的设计方法。最后,通过例子对所得结论加以说明。     

变采样周期网络控制系统的非脆弱保性能控制

研究了一类具有随机时延和控制器增益扰动的非线性网络控制系统的非脆弱保性能控制问题。基于变采样周期的方法,将网络控制系统建模为非线性Markov跳变系统。利用Lyapunov稳定性理论,给出了保证整个闭环系统均方随机渐近稳定的充分条件。通过线性矩阵不等式的方法,设计了一种非脆弱状态反馈控制器,在该控制器的作用下,闭环系统的能量函数值不超过一个规定的上界。仿真算例说明了所提方法的有效性。     

Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system

This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS). Based on the parallel distributed compensation (PDC) approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations. The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities (BMIs). The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.     

Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems

A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.     

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality (LMI) via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.     

精馏塔极小极大鲁棒非脆弱控制的研究

将极小极大控制器的设计应用于精馏塔模型。考虑系统和控制器同时含有不确定性,利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,设计了鲁棒且非脆弱的极小极大控制器。考虑不确定性对系统破坏最大的情形,分别给出含有加性和乘性干扰增益的控制器存在条件。引入凸优化算法,求解使闭环系统渐近稳定且性能指标上界最小的最优控制器参数。仿真结果表明所设计的控制器具有良好的鲁棒性和非脆弱性。     

T-S模糊时滞系统的鲁棒无源控制

基于Lyapunov稳定性理论,时具有参数不确定性的T-S模糊时滞系统的鲁棒稳定性和无源性进行了研究.具有参数不确定性的T-S模糊模型可以任意精度近似连续非线性不确定系统.假设系统中的参数不确定性是范数有界的.运用Lyapunov稳定性理论给出了鲁棒无源控制器存在的充分条件.通过解一组线性矩阵不等式(LMIs),可直接获得鲁棒无源控制器.所设计的鲁棒无源控制器能够保证对于T-S模糊时滞系统中所有的参数不确定性,闭环系统都是鲁棒稳定的并且是严格无源的.并且,通过求解带有约束条件的线性矩阵不等式问题,可以设计出具有最大耗散率的鲁棒无源控制器.数值例子验证了所提出设计方法的有效性.