A DETERMINISTIC AFFINE-QUADRATIC OPTIMAL CONTROL PROBLEM

    Authors

    Y. C. Wang;J. M. Yong

    Comments

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    Abbreviated Journal Title

    ESAIM-Control OPtim. Calc. Var.

    Keywords

    Affine quadratic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; quasi-Riccati equation; state feedback; representation; STOCHASTIC DIFFERENTIAL-EQUATIONS; RICCATI EQUATION; SYSTEMS; Automation & Control Systems; Mathematics, Applied

    Abstract

    A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton-Jacobi-Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional conditions, it is shown that the value function is actually twice differentiable and the so-called quasi-Riccati equation is derived, whose solution can be used to construct the state feedback representation for the optimal control.

    Journal Title

    Esaim-Control Optimisation and Calculus of Variations

    Volume

    20

    Issue/Number

    3

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    633

    Last Page

    661

    WOS Identifier

    WOS:000337948200001

    ISSN

    1292-8119

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