一类多输入定常系统LQ最优控制的研究

On the LQ Optimal Control for a Class of Multi-InputTime-Unvariable Systems

基于求解 Riccati方程 ,研究了一类定常多输入系统的 LQ最优控制问题 ,给出了当加权矩阵 R具有某种形式时 ,其最优控制律可转化为求解单输入系统的 LQ最优控制律而获得 .

The LQ optimal control problem could be solved directly by solving the Riccati equation. It could be solved according to the frequency equality also. This paper studied the LQ optimal control problem of a class of multi input time unvariable systems. Based on solving Ricaati equation, when the weight matrix R has some special structures, the optimal control law of multi input time unvariable systems could be obtained by solving the LQ optimal control problem of single input systems. Because the way of solving the LQ optimal control problem of single input systems is more easier than solving the multi input systems, so there are some value of theory and application for the results presented in this paper.