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

TL;DR

The paper tackles constrained control of linear systems under time-varying and a priori unknown cost functions with pointwise state and input constraints. It blends online convex optimization with a reference governor, applying online gradient descent to track the time-varying optimal steady state and uses a $\\lambda$-contractive set to enforce feasibility. The authors prove recursive feasibility, constraint satisfaction at all times, and a dynamic regret that scales linearly with the variation of the cost functions, validating the approach via a simulation. This work provides principled guarantees for constrained control under shifting objectives, with potential extensions to disturbances.

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 $λ$-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.

Figures (1)

• Figure 3: Closed-loop trajectories of the simulation example.