Online Nonstochastic Control with Convex Safety Constraints

TL;DR

This paper introduces OGD-BZC, an online control algorithm that ensures safety constraints are always met in linear systems with adversarial disturbances, while achieving sublinear regret.

Contribution

The paper presents a novel online control algorithm that guarantees safety constraints and achieves $ ilde{O}( oot{T} ull)$ regret in adversarial settings.

Findings

OGD-BZC satisfies all safety constraints under bounded disturbances.

The algorithm achieves $ ilde{O}( oot{T} ull)$ regret.

Numerical results demonstrate robustness and effectiveness.

Abstract

This paper considers the online nonstochastic control problem of a linear time-invariant system under convex state and input constraints that need to be satisfied at all times. We propose an algorithm called Online Gradient Descent with Buffer Zone for Convex Constraints (OGD-BZC), designed to handle scenarios where the system operates within general convex safety constraints. We demonstrate that OGD-BZC, with appropriate parameter selection, satisfies all the safety constraints under bounded adversarial disturbances. Additionally, to evaluate the performance of OGD-BZC, we define the regret with respect to the best safe linear policy in hindsight. We prove that OGD-BZC achieves $\tilde{O} (\sqrt{T})$ regret given proper parameter choices. Our numerical results highlight the efficacy and robustness of the proposed algorithm.