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.

Optimal Guaranteed Cost Control for Discrete Time Uncertain Time-Delay Systems with Control Input Constraints

For a class of discrete-time state delay systems with norm-bounded time-varying parameter uncertainty and control input constraints, this paper addresses the problem of designing an optimal guaranteed cost state feedback controller. A condition for the existence of guaranteed cost controllers is derived. Furthermore, it is shown that this condition is equivalent to the feasibility problem of a certain linear matrix inequality system, and its solutions provide a parametrized representation of guaranteed cost controllers. Based on that fact, the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally, an example is given to illustrate the proposed results.