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J. Korean Math. Soc. 1998; 35(1): 115-126

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

Optimal problem of regular cost function for retarded system

Jong-Yeoul Park, Jin-Mun Jeong, and Young-Chel Kwun

Pusan National University, Pukyong National University and Dong-A University

Abstract

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We study the optimal control problem of system governed by retarded functional differential $$ x^{'}(t)= A_0x(t)+ A_1x(t-h)+ \int_{-h}^0 a(s)A_2x(t+s)ds + B_0u(t) $$ in Hilbert space $H$. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

Keywords: optimal control problem, retarded functional differential equation, maximal principle, bang-bang principle

MSC numbers: Primary 49B20; Secondary 93C20

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