跟踪问题最优控制律精细积分

 构成有限时间最优跟踪系统的控制律需要求解 Riccati微分方程及外部控制输入向量满足的微分方程 ,前者是非线性矩阵微分方程 ,后者是变系数线性微分方程。在结构力学与最优控制的模拟理论基础上所发展的精细积分方法借鉴了计算结构力学中的算法 ,可以精确有效地求解这些微分方程。这种方法的特点之一在于步长幅度变化较大时 ,Riccati微分方程的数值解仍可以保持很高的精度 ,并且变系数线性微分方程的求解亦可纳入其体系而不必用通常的差分方法。本文介绍了用精细积分方法求解这些方程的过程 ,并给出了数值算例。

PRECISE INTEGRATION FOR CONTROL LAW OF OPTIMAL TRACKING

To obtain the control law of finite\|horizon optimal tracking problems, the Riccati differential equation and the differential equation of the external driving function must be solved at first. The former is a nonlinear matrix differential equation and the latter is a linear time varying one. The precise integration method, which is based on the theory of analogy between structural mechanics and optimal control, can be employed to solve these differential equations precisely and efficiently. This method borrows ideas from the algorithm of computational structural mechanics. One distinguishing feature of the method is that great change of step\|size almost does not affect the precision of the numerical solution of Riccati differential equation. Another feature is that the linear time varying differential equation of the external driving function can also be solved by this method instead of the usual finite difference method. Both the process of implementing the precise integration and the numerical example are presented in this paper.