论文部分内容阅读
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
The control law that forms the optimal tracking system for a finite time needs to solve the differential equation satisfying the Riccati differential equation and the external control input vector. The former is a nonlinear matrix differential equation and the latter is a variable coefficient linear differential equation. The precise integration method developed on the basis of simulation theory of structural mechanics and optimal control draws on algorithms in structural mechanics to solve these differential equations accurately and effectively. One of the characteristics of this method is that the numerical solution of the Riccati differential equation can still maintain a high accuracy when the step size changes greatly and the solution of the variable coefficient linear differential equation can also be incorporated in the system without using the usual difference method . This article describes the process of solving these equations using the exact integral method, and gives a numerical example