故障系统控制律重构的代数黎卡提方程方法

An Algebraic Riccati Equation Approach to Restructurable Control for Failed Systems

该文考虑故障系统的控制律重构问题，即重新设计控制律，使重构后的控制系统满足如下条件：（１）与重构前系统的误差（范数意义下）极小；（２）与重构前系统具有相同的稳定裕度；（３）控制能量极小。研究结果表明，上述综合指标约束下的控制律重构问题可转化为求解一代数黎卡提方程，并因此得到完整的解决。文中对一类代数黎卡提方程的求解算法做了相应的讨论，并提供了说明性的数值算例。理论分析及仿真结果都说明了该文所提设计方法的直接性和有效性。

In this paper the problem of redesigning controller for failed systems is considered. The aim of this problem is to redesign the controller such that the restructured system satisfies the following requirements:1) minimizing the error norm of closed loop system matrices between the nominal and the failed model; 2) possessing the same stability margin as the nominal system; and 3) minimizing the control energy. It is shown that the problem of redesigning control law with mixed performance constraints can be converted to the problem of solving an algebraic Riccati equation, and thus this problem is solved completely. The numerical algorithm for solving a class of algebraic Riccati equations is discussed,and the illustrative example is also provided. Both the theoretical analysis and the simulation result show that the proposed design method is direct and effective.