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

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.

Online Linear Quadratic Tracking with Regret Guarantees

“…In cases where a window of predictions is available, a receding horizon gradient descent algorithm is suggested in [3] with a dynamic regret analysis. In a more recent line of work [4], the authors introduce a memory based, gradient descent algorithm and in [5], tackle the constrained tracking problem with policy regret guarantees. In [6], the authors analyze the output tracking scheme of an iterative learning controller and provide dynamic and static regret bounds.…”

Online Linear Quadratic Tracking With Regret Guarantees

“…The LQT problem for sequentially revealed adversarial reference states is studied mostly with policy regret guarantees, with one of the first works [3] suggesting a relatively computationally heavy algorithm. In a more recent line of work [4], the authors introduce a memory-based, gradient descent algorithm and in [5], tackle the constrained tracking problem. Several works also provide dynamic regret guarantees for tracking of unknown targets, however, their settings differ from ours.…”