An online convex optimization algorithm for controlling linear systems with state and input constraints

TL;DR

This paper introduces an online convex optimization algorithm tailored for controlling linear systems with state and input constraints, capable of handling time-varying costs while ensuring constraint satisfaction and achieving sublinear regret.

Contribution

The paper proposes a novel online gradient descent-based algorithm for constrained linear control systems with theoretical performance guarantees.

Findings

Achieves sublinear dynamic regret under certain conditions.

Ensures constraint satisfaction throughout control.

Demonstrates effectiveness through a practical example.

Abstract

This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost functions while restraining the system states and inputs to polytopic constraint sets. Analysis of the algorithm's performance, measured by dynamic regret, reveals that sublinear regret is achieved if the variation of the cost functions is sublinear in time. Finally, we present a simple example to illustrate implementation details as well as the algorithm's performance and show that the proposed algorithm ensures constraint satisfaction.