有限时间信息融合线性二次型最优控制

Finite-time information fusion for linear quadratic optimal control

针对有限时间线性二次型最优控制问题,提出了一种新的求解方法—–信息融合估计方法.基于线性最小方差估计准则下的融合估计理论,通过融合期望状态轨迹、理想控制策略等软约束信息,分别采用集中式融合和序贯式融合两种信息处理方法,求得最优状态调节器问题的最优融合控制序列.进一步从理论上论证了序贯式融合控制方法与传统最优控制方法的一致性,并通过直流电机系统的数值仿真也验证了集中式和序贯式融合控制方法与传统最优控制方法的等效性,从而统一了最优估计与最优控制问题,并为最优控制问题提供了一种新的求解方法.

For the finitetime linear quadratic optimal control problem, we propose a novel solving method informa tion fusion estimation method. Based on the fusion theory with minimum variance linear estimation criterion, the informa tion of the desired state trajectory and the desired control strategy is fused to obtain the optimal fusion control sequence for the optimal state regulator by using the centralized and the sequential information fusion methods, respectively. The consistency between the sequential information fusion control method and the traditional optimal control method is theo retically proved. Numerical simulation results of a DC motor system show the equivalence of the centralized fusion control method, the sequential fusion control method and the traditional optimal method, thus unifying the optimal estimation and the optimal control and providing a novel method for optimal control problem.