Online convex optimization for constrained control of linear systems using a reference governor

TL;DR

This paper introduces a control scheme combining online convex optimization and a reference governor to manage constrained linear systems with time-varying costs, ensuring feasibility, constraint satisfaction, and bounded regret.

Contribution

It develops a novel control approach that guarantees recursive feasibility, constraint satisfaction, and bounded dynamic regret for linear systems under unknown, changing cost functions.

Findings

The proposed method guarantees recursive feasibility and constraint satisfaction.

It achieves a linearly bounded dynamic regret relative to cost function variation.

Simulation results demonstrate the effectiveness of the control scheme.

Abstract

In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex optimization and a reference governor. In particular, we apply online gradient descent to track the time-varying and a priori unknown optimal steady state of the system. Moreover, we use a $\lambda$-contractive set to enforce constraint satisfaction and a sufficient convergence rate of the closed-loop system to the optimal steady state. We prove that the proposed scheme is recursively feasible, ensures that the state and input constraints are satisfied at all times, and achieves a dynamic regret that is linearly bounded by the variation of the cost functions. The algorithm's performance and constraint satisfaction is illustrated by means of a simulation example.