时延数字控制系统最优控制问题的离散正交多项式解法

本文利用一般的离散正交多项式研究了具有2s个时延项离散系统的最优控制问题。文中导出了系统状态和控制向量离散正交级数展开式中系数向量间的关系,然后,将离散动态系统的最优控制问题转化为直接对二次型性能指标中一组系数向量的参数优化问题,并由一组线性代数方程给出了这组最优系数向量的解。最后,还介绍了一个数值例子。

Approximation Solution for Optimal Control Problems Time-Delay Digital Systems Via Discrete Orthogonal Polynomials

In this paper, optimal control problem of time-delay digital control system has been studied using discrete orthogonal polynomials.The relationship between the state coefficient vector and control coefficient vector is obtained. The discrete orthogonal polynomials are used to modify the optimal equations into a set of linear algebraic ones for the approximate solutions of optimal state and control variables. Finally, a practical example is given by using discrete Chebyshev polynomial, discrete Laguerre polynomial and discrete Legendre polynomial, and the results obtained are satisfactoy.