PIECEWISE LINEAR-APPROXIMATION FOR HEREDITARY CONTROL-PROBLEMS

作     者：PROPST, G 

作者机构：NASALANGLEY RES CTRINST COMP APPL SCI & ENGNHAMPTONVA 23665 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：1990年第28卷第1期

页      面：70-96页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：34K35 65L60 93C15 hereditary control problem piecewise linear approximation uniform stability 

摘      要：This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimjzed subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space $\mathbb{R}^n \times L^2 $ and the favorable eigenvalue behavior of the piecewise linear approximations.