Approximate solution of the HJB inequality related to the infinite horizon optimal control problem with discounting

Vladimir Gaitsgory, Serguei Rossomakhine, N Thatcher

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    This paper is focusing on finding smooth approximate solutions of the HJB inequality that corresponds to the infinite horizon optimal control problem with discounting. We establish that such approximate solutions exist (under a simple controllability type condition) and that they can be used for construction of near optimal controls. We also show that these approximate solutions of the HJB inequality can be found by solving certain semi-infinite linear programming problems and we propose an algorithm for the solution of the latter. We discuss a numerical solution of a non-trivial optimal control problem obtained with the help of a software implementation of the new algorithm.

    Original languageEnglish
    Pages (from-to)65-92
    Number of pages28
    JournalDynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and Algorithms
    Volume19
    Issue number1-2b
    Publication statusPublished - 2012

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