线性二次极小极大最优反馈控制的同步并行解法及充要条件

CONCURRENT PARALLEL ALGORITHM AND NECESSARY AND SUFFICIENT CONDITION FOR MAXMIN OPTIMAL FEEDBACK CONTROL OF LINEAR QUADRATIC

在线性系统鲁棒控制及H∞ 时域直接状态空间方法中 ,化为线性二次型 (LQ)极小极大 (MAXMIN)最优状态反馈控制问题是其方法之一。本文给出的线性二次极小极大最优反馈控制的同步并行解法克服了先寻极大这种逐次寻优算法的困难。而且 ,只需存在 (增广系统 )Riccati一般矩阵代数方程的对称镇定解 ,即可获得充分且必要条件的最优反馈控制及抑制干扰 (反馈 )

The problem of maxmin optimal state feedback control of linear quadratic is one of the methods that deal with robust control and time domain H ∞ direct state space method of linear system.In this paper,concurrent parallel algorithm for maxmin optimal feedback control of linear quadratic is presented,which bridges the difficulty of the gradual and optimal algorithm(first max then min,of first min then max).Moreover,if there is the symmetric stabilization solution of the matrix algorithm Riccati equation,we gain the necessary and sufficientcondition for maxmin optimal feedback control of linear quadratic.