传感器失效下不确定离散时滞系统的静态输出反馈鲁棒可靠保成本控制

针对一类参数不确定离散时滞系统,研究了当传感器发生增益故障情况下的静态输出反馈保成本可靠控制器设计问题.系统中的参数不确定性满足广义匹配条件,传感器元件具有部分输出增益故障.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了含有时滞记忆和无时滞静态输出反馈保成本鲁棒可靠控制律的存在条件.通过求解由一组线性矩阵不等式所表示的凸优化问题可以得到使得闭环保成本上界最小的鲁棒可靠控制器.最后通过仿真示例说明所提出方法的正确性.     

不确定随机时滞系统的鲁棒H∞保性能控制

讨论了一类具有时变时滞的不确定It类型随机系统的鲁棒H∞保性能控制问题. 运用Lyapunov-Krasovskii泛函方法, 设计使得闭环系统鲁棒随机指数均方稳定, 且具有给定H∞干扰抑制度 γ 的状态反馈保性能控制器. 控制器存在的充分条件以线性矩阵不等式(LMIs)的形式表示. 进一步, 通过求解具有LMIs约束的凸优化问题, 给出了不确定随机时滞系统的最优保性能控制器的设计方法. 最后通过一个数值例子验证了所提方法的有效性.     

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.     

不确定线性时滞系统的一种混杂状态反馈保成本控制及优化设计方法

本文研究一类不确定线性时滞系统的混杂状态反馈保成本控制及优化设计问题.假设存在有限个备选的控制增益已知的控制器,并且其中任何单一的状态反馈控制器都不能镇定系统,基于单Lyapunov函数的方法,给出了混杂状态反馈保成本控制的充分条件及优化设计方案.当备选的控制增益未知时,利用多Lyapunov函数法,同样给出混杂状态反馈保成本控制的充分条件及相应的优化设计方法.最后用仿真验证了文中方法的有效性.     

Minimax guaranteed cost control of uncertain non-linear systems

In this paper, a guaranteed cost control for non-linear uncertain systems is developed. The relationship between the idea of guaranteed cost control and dissipative feedback is first discussed which have been independently studied in the literature on robust control. It turns out that the two approaches are equivalent, and both presume the existence of a storage function (a Lyapunov function candidate) which guarantees the stability of the closed-loop system. The idea of guaranteed cost control is then applied to solve the robust control problem for non-linear systems with both drift vector field and input vector field uncertainties. Necessary and sufficient conditions are given for the solvability of this problem in terms of certain Hamilton-Jacobi Isaac's inequalities. The robustness properties of the controllers are also discussed. Finally, a passivity-based approach to the synthesis of guaranteed cost controllers is discussed.     

基于状态观测器的线性不确定时滞系统的保代价控制

研究一类线性不确定时滞系统，基于状态观测器给出了系统保代价控制的无记忆状态反馈控制器，并给出了保代价控制器存在的充分条件，在某些条件满足的条件下，基于LMI给出了系统保代价控制器。     

时变不确定多时滞连续系统的最优保成本控制

针对一类同时具有状态多时滞和输入多时滞的时变不确定连续多时滞系统。研究保成本状态反馈控制器的设计。假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件,通过构造改造的Lyapunov函数和线性矩阵不等式（LMI）方法,给出系统满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界。通过求解凸优化问题得到最优保性能控制器,最后用数值例子说明该方法的有效性。     

Non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems

1 Introduction In recent years, the switched control systems have been attracting considerable attention in the control commu- nity [1～7]. Basically, a switched system belongs to a spe- cial class of hybrid systems, which consist of a family of continuous-time or discrete-time subsystems and a switch- ing law that specifies the switching between them. Such control systems appear in many applications, such as com- municatin networks, switching power converters and many other fields. On the oth…     

线性不确定系统的最优保性能控制--线性矩阵不等式处理方法

针对一类具有范数有界时变参数不确定性的线性系统的和一个给定的二次型性能指标,研究了其最优保性能控制问题,用一个线性矩阵不等式系统的可解性给出了存在保性能状态反馈控制律的条件,并且这个线性矩阵不等式系统的可行解提供了一组保性能控制律的一个参数化表示,进而保性能控制律的这一刻划被用来求解最优保成本控制问题。     

Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.     

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.     

时变不确定切换广义系统的鲁棒最优保性能控制

针对一类时变参数不确定切换广义系统,对其鲁棒最优保性能控制问题进行研究,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件。通过构造广义Lyapunov函数和线性矩阵不等式方法,给出系统鲁棒最优保性能控制器存在的充分条件。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到鲁棒最优保性能控制律及闭环性能指标上界。最后用示例说明该方法的有效性。     

An Lmi Approach To Non‐Fragile Guaranteed Cost Control Of Uncertain Discrete Time‐Delay Systems

This paper studies the non‐fragile Guaranteed Cost Control (GCC) problem via memoryless state‐feedback controllers for a class of uncertain discrete time‐delay linear systems. The systems are assumed to have norm‐bounded, time‐varying parameter uncertainties in the state, delay‐state, input, delay‐input and state‐feedback gain matrices. Existence of the guaranteed cost controllers are related to solutions of some linear matrix inequalities (LMIs). The non‐fragile GCC state‐feedback controllers are designed based on a convex optimization problem with LMI constraints to minimize the guaranteed cost of the resultant closed‐loop systems. Numerical examples are given to illustrate the design methods.     

改进的网型结构电力系统鲁棒重叠分散控制

研究一类多区域互联电力系统的特殊重叠分解及其鲁棒分散控制问题,提出一种新的互联电力系统重叠分解的方法。该方法根据电力系统本身的结构信息约束和大系统包含原理的约束条件,对系统进行重叠分解处理,使原系统扩展成为两两子系统;然后,在有机结构控制(OSC)的线性矩阵不等式(LMI)方法的基础上,为系统设计了改进的鲁棒分散控制器。以一个4区域网型结构电力系统为例进行仿真研究,其结果表明,所设计的控制器较直接使用LMI方法能使系统具有更令人满意的控制性能。     

Resilient guaranteed cost control for uncertain discrete linear jump systems

Robust stochastic stabilization and guaranteed cost control for a class of uncertain discrete-time linear system with Markovian jumping parameters are discussed. Two classes of controller gain perturbations, additive and multiplicative, are considered. The necessary and sufficient conditions for the above problems are derived, which are in terms of positive-definite solutions of a set of coupled linear matrix inequalities (LMIs). Furthermore, resilient guaranteed cost controllers are designed. Finally, numerical examples are presented to illustrate the solvability and effectiveness of the results.     

Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay

This paper considers the guaranteed cost control problem for a class of uncertain discrete T-S fuzzy systems with time delay and a given quadratic cost function. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequalities （LMI） approach by constructing a specific nonquadratic Lyapunov-Krasovskii functional and a nonlinear PDC-like control law. A convex optimization problem is also formulated to select the optimal guaranteed cost controller that minimizes the upper bound of the closed-loop cost function. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.     

不确定离散时间系统积分滑模保性能控制

针对不确定离散时间系统,研究其积分滑模（ＩＳＭ）保性能控制的设计问题．将最优保性能积分滑模面设计问题,转化为一个具有线性矩阵不等式（ＬＭＩ）约束的目标函数凸优化问题,给出了最优保性能积分滑模面存在的充分条件,并结合干扰估计器设计相应的保性能控制器．与传统滑模控制相比较,积分滑模保性能控制系统具有全阶滑动模态,系统的鲁棒性得到加强,消除了控制抖振和稳态抖振．仿真结果验证了该方法的有效性．     

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.     

一类参数不确定时滞系统的保成本控制

通过构造参数相关的李雅普诺夫函数,利用S-procedure方法研究一类具有参数不确定性和状态滞后的线性动态系统,得到了这类不确定时滞系统存在保成本控制器的充分条件.     

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。