Title

A Deterministic Affine-Quadratic Optimal Control Problem

Keywords

Affine quadratic optimal control; Dynamic programming; Hamilton-Jacobi- Bellman equation; Quasi-Riccati equation; State feedback representation

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. © EDP Sciences, SMAI, 2014.

Publication Date

1-1-2014

Publication Title

ESAIM - Control, Optimisation and Calculus of Variations

Volume

20

Issue

3

Number of Pages

633-661

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1051/cocv/2013078

Socpus ID

84903608374 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84903608374

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