The generalised continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control

TL;DR

This paper explores the role of the continuous-time generalized Riccati equation in singular LQ optimal control, demonstrating that symmetric solutions lead to impulse-free optimal controls, thus clarifying its significance.

Contribution

It establishes the connection between symmetric solutions of the generalized Riccati equation and the existence of impulse-free optimal controls in continuous-time singular LQ problems.

Findings

Symmetric solutions of the generalized Riccati equation imply impulse-free optimal controls.

The paper clarifies the importance of the generalized Riccati equation in continuous-time LQ control.

It extends understanding of singular LQ problems and their solutions.

Abstract

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the discrete-time generalised Riccati equation, but, differently from the discrete case, to date the importance of this equation in the context of optimal control is yet to be understood. This note addresses this point. We show in particular that when the continuous-time generalised Riccati equation admits a symmetric solution, the corresponding linear-quadratic (LQ) problem admits an impulse-free optimal control.