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

作　　者：张宝琳[1] 郑菲菲[1] 唐功友[2] 

机构地区：[1]中国计量学院理学院,杭州310018 [2]中国海洋大学信息科学与工程学院,山东青岛266100

出　　处：《控制与决策》2012年第5期691-696,共6页Control and Decision

基　　金：国家自然科学基金项目(60874029;40776051);浙江省自然科学基金项目(Y107232;Y1110036)

摘　　要：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.

关 键 词：奇异摄动系统 时滞 次优控制 CHEBYSHEV多项式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]