On Riccati contraction in time-varying linear-quadratic control

TL;DR

This paper investigates the contraction properties of the Riccati operator in non-stationary linear-quadratic control, providing bounds on convergence rates using a lifting approach under controllability and observability assumptions.

Contribution

It introduces a novel lifting method to bound Riccati operator contraction rates in time-varying LQ control, linking these rates to controllability and observability conditions.

Findings

Bound on the rate of strict contraction established

Contraction rate depends on controllability and observability

Lifting approach effectively analyzes non-stationary Riccati dynamics

Abstract

Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian metric, across a sufficient number of iterations. This number of iterations is related to an assumed uniform controllability and observability property of the dynamics and stage-cost in the original formulation of the problem.