A Deterministic Affine-Quadratic Optimal Control Problem

TL;DR

This paper investigates a deterministic affine-quadratic optimal control problem, establishing conditions for optimal controls, differentiability of the value function, and deriving a quasi-Riccati equation with feedback control representation.

Contribution

It introduces a quasi-Riccati equation for the problem and shows the value function's differentiability, enabling classical Hamilton-Jacobi-Bellman solutions.

Findings

Optimal controls exist under mild conditions

Value function is differentiable under certain assumptions

Optimal controls can be expressed via a state feedback law

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 value function is differentiable and therefore satisfies the corresponding Hamilton-Jacobi-Bellman equation in the classical sense. Moreover, the so-called quasi-Riccati equation is derived and any optimal control admits a state feedback representation.