具有控制约束的不确定离散系统最优保性能控制

Optimal guaranteed cost control for uncertain discrete-timelinear systems with input constraints

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。

For a class of discrete-time linear systems with norm-bounded time-varying parameter uncertainty and control input constraints, 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. On this basis, the design problem of the optimal guaranteed cost controller for uncertain discrete-time systems 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.