奇异摄动时滞系统次优控制的Chebyshev多项式级数方法

Chebyshev polynomial series method of suboptimal control for singularly perturbed time-delay systems

研究奇异摄动时滞系统次优控制的近似设计问题.基于奇异摄动的快慢分解理论,将系统的最优控制问题转化为无时滞快子问题和线性时滞慢子问题;利用Chebyshev多项式级数方法将时滞慢子问题的近似求解问题转化为线性代数方程组的求解问题,进而得到原系统的次优控制律,该控制律由Chebyshev多项式级数的基向量表示.仿真算例表明了该方法的有效性.

This paper studies an approximation approach to optimal control for singularly perturbed time-delay systems. Based on the slow-fast decomposition theory of singular perturbation,the optimal control problem is firstly decomposed into a fast subproblem and a slow one with time-delay.By using Chebyshev polynomial series method,the optimal control law design of the slow one is transformed into a problem of solving linear equations.Then,a suboptimal control law of the slow subproblem is developed by solving the linear equations.Further,the suboptimal control law of the original problem is obtained and formulated as base vectors of the Chebyshev polynomial series.Numerical example is presented to show the effectiveness of the proposed method.