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。

Reliable Guaranteed Cost Control for Uncertain Singular Systems

In this paper the problem of reliable guaranteed cost control for a class of uncertain singular systems with actuator failures is dealt with. The parameter uncertainties in the state matrix are assumed to be time-varying and norm-bounded. The purpose of the problem is to design a state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring in the prespecified subset of actuators, the plant keeps regular, impulse-free and stable, and an adequate level of a quadratic cost index can be guaranteed. A sufficient condition for the existence of reliable guaranteed cost controller is derived. Furthermore, it is shown that a group of linear matrix inequalities provide a parameterized representation of reliable guaranteed cost controllers. Based on this, the design problem of the optimal reliable 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.