模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

离散T-S模糊系统的部分状态反馈H∞控制

基于部分状态信息的控制器是一类特殊的静态输出反馈控制器,一般难以利用线性矩阵不等式工具求解.本文研究离散T-S模糊系统的部分状态反馈镇定及部分状态反馈H∞控制问题.通过引入松弛变量,将离散T-S模糊系统的部分状态反馈镇定问题转换成求解一组线性矩阵不等式（LMI）,并给出基于LMI的部分状态反馈H∞控制器设计方法.通过数值算例验证了所给方法的有效性.     

基于LMI方法的离散分段线性系统静态输出反馈控制

研究了离散分段线性系统静态输出反馈控制问题. 基于分段二次李亚普诺夫函数, 给出了静态输出反馈镇定控制器综合的新的充分的线性矩阵不等式条件. 同时, 通过使用Finsler引理, 引入一组具有特殊结构的松弛变量以减少设计保守性. 与以后方法相比, 所提出的方法具有好的性能, 并且在已有方法失效的情况下仍可用. 文中还将此方法推广到H无穷控制. 最后给出三个例子说明方法的有效性.     

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本文研究了用Lur'e多非线性系统描述的被控对象的镇定问题.把问题的可解性归结到特殊的多线性矩阵不等式的可解性.非线性状态反馈和输出反馈控制器的设计分别依赖于一个双线性和三个三线性矩阵不等式的解.给出了基于线性矩阵不等式的交替寻优算法的设计步骤.     

基于部分状态信息的模糊控制器设计

基于部分状态信息的控制器是一类特殊的静态输出反馈控制器,一般难以利用线性 矩阵不等式工具求解.该文研究了Takagi-Sugeno模糊模型的部分状态反馈控制问题,设计问 题可以归结为求解一组双线性矩阵不等式.通过使控制器增益由全状态反馈变化为部分状态 反馈,这类双线性矩阵不等式可以利用同伦算法求解.从而,镇定模糊部分状态反馈控制器可 以通过迭代方法得到.仿真例子验证了算法的有效性.     

最小阶输出反馈镇定控制器设计*

本文首先基于逆ＬＱＧ方法得到了静态输出反馈可镇定的一种充要条件，并进一步给出了固定输出反馈可镇定的充要条件和控制器的设计方法，基于此给了一种最小阶镇定控制器的设计方法，这些条件的形式简单，判断其可镇定性和设计镇定控制器仅需解几个相应的矩阵不等式。     

＋不确定连续系统线性二次型次优控制问题的研究

基于静态输出反馈研究了不确定连续系统线性二次型（LQ）次优控制问题,应用线性矩阵不等式（LMI）给出了问题可解的充分条件,设计出了输出反馈控制器,保证了闭环系统的稳定。最后给出了仿数值算例说明该方法的有效性。     

Lur'e系统镇定问题的非线性控制器设计

本语文研究了用Ｌｕｒ‘ｅ多非线性系统描述的被控对象的镇定问题,把问题的可解笥归结到特殊的多线性矩阵不等式的的可解性,非线笥状态反馈和输出反馈控制器的设计分别依赖于一个双线性和三个三线性矩阵不等式的解,给出了基于线性矩阵不等式的交替寻优算法的设计步骤。     

Lur'e多非线性系统的镇定与L2-增益控制的MI方法

考虑Lur'e多非线性系统的镇定与L2-增益控制问题.对Lur'e多非线性系统表示 控制对象,设计状态反馈和输出反馈控制器使闭环系统分别是绝对稳定和L2增益有限的.基 于矩阵不等式(MI)方法给出了镇定与L2-增益控制问题的可解条件,并讨论了控制器的设计 方法.     

基于结构L yapunov 矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题，这导致了一个非线性最优化问题，是无法直接求解的．针对线性时不变系统(LTI)，深入研究这两个矩阵不等式的关系，通过构造一个结构Lyapunov矩阵，给出了一个问题有解的充分条件，并在此基础上提出一个静态输出反馈镇定算法．利用线性矩阵不等式(LMI)方法，可直接求解出相应的输出反馈增益．数值实例证明了该方法的有效性．     

同时镇定：逆LQ方法

本文使用逆ＬＱ方法了同时镇定问题，首先得到了ｒ个正则ＭＩＭＯ对象可静态输出反馈同时定的充要条件，然后给出了状态反馈问题同时镇定的一种解，这些条件均以一组耦合Ｒｉｃｃａｔｉ方程和Ｒｉｃｃａｔｉ不等式的形式给出，本语文证明，任一同时镇定反馈增益均可描述为一组具有合适交叉项的耦合ＬＱ控制问题的解。     

Simultaneous linear-quadratic optimal control design via static output feedback

In this paper, the problem of designing a fixed static output feedback control law which minimizes an upper bound on linear quadratic (LQ) performance measures for r distinct MIMO plants is addressed using linear matrix inequality (LMI) technique. An iterative LMI algorithm is proposed to obtain the solution. Examples are used to demonstrate its effectiveness. Copyright ©1999 John Wiley & Sons, Ltd.     

线性二次型指标下的最优输出反馈问题

本文研究了线性二次型指标下的最优输出反馈问题。根据系统参数,在二次型指标中适当选择状态加权矩阵Q可以将LQ问题的状态反馈解表成输出反馈的形式。文中给出了这种输出反馈解存在的充分性条件。     

Linear quadratic control with stability degree constraint

The problem of static state feedback Linear Quadratic (LQ) optimal control subject to a prescribed degree of stability for the closed-loop system is considered in this paper. A necessary optimality condition is given via the Lagrange multiplier method. A globally convergent algorithm is provided to solve the optimization problem. It is shown that the algorithm recovers the standard LQ feedback gain provided the desired stability degree is small enough to be within the range by the standard LQ design. As for other cases the optimum occurs on the boundary of the α-region. A numerical example shows that the proposed algorithm provides a better design compared to the existing methods.     

Computational methods for parametric LQ problems--A survey

Iterative methods for finding the optimal constant feedback gains for parametric LQ problems, notably for optimal constant output feedback problems, are surveyed. The connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties. Especially, the descent Anderson-Moore method, Levine-Athans like methods, and the Newton method are considered. Convergence results are also included. The initialization problem and the output feedback stabilization problem are also discussed. Furthermore, it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric LQ problems as well, notably so-called robust parametric LQ problems.     

Some new results on optimal and suboptimal regulators of the LQproblem with output feedback

The LQ (linear quadratic) regulator problem with output feedback is considered. In the problem studies an output feedback control is determined such that the cost is J*, the optimal cost for the LQ problem with state feedback, or βj* with some constant β>1. A set of sufficient conditions is given for determining such optimal and suboptimal output feedback control laws     

Suboptimal Strategies of Linear Quadratic Closed-loop Differential Games: An BMI Approach

The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB, An example is given to illustrate the proposed results.     

线性二次闭环微分对策次优对策的双线性矩阵不等式方法

The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results.     

Guaranteed cost control for networked control systems

The guaranteed cost control problem for networked control systems (NCSs) is addressed under conmmnication constraints and varying sampling rate. First of all, a simple inFormation-scheduling scheme is presented to describe the scheduling approach of system signals in NCSs. Then, based on such a scheme and given sampling method, the design procedure in dynarmic output feedback manner is also derived which renders the closed loop system to be asymptotically stable and guarantees an upper bound of the LQ pefformance cost function.     

一类奇异时滞系统的奇异二次指标最优控制问题

利用基本的代数等价变换，将一类奇异滞后系统的奇异二次指标最优控制问题转化为正常状态滞后系统的非奇异二次指标最优控制问题，并讨论了二的等价性，在一些常规条件下，给出了问题的解，并把最优控制综合为最优状态反馈。