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A deterministic affine-quadratic optimal control problem∗

Published online by Cambridge University Press:  21 May 2014

Yuanchang Wang  and
Jiongmin Yong
Yuanchang Wang
Affiliation:
School of Mathematics, Yunnan Normal University, Kunming, 650500, P.R. China Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA. [email protected]
Jiongmin Yong
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA. [email protected]
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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.

Keywords

Affine quadratic optimal controldynamic programmingHamilton–Jacobi–Bellman equationquasi-Riccati equationstate feedback representation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 3 , July 2014 , pp. 633 - 661
Copyright
© EDP Sciences, SMAI, 2014

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