Safe Non-Stochastic Control of Control-Affine Systems: An Online Convex Optimization Approach

TL;DR

This paper introduces an online convex optimization algorithm for safely controlling nonlinear control-affine systems under unknown, bounded non-stochastic noise, ensuring safety and bounded regret in complex, real-world scenarios.

Contribution

It presents a novel control algorithm that guarantees safety and bounded regret for control-affine systems facing adversarial noise, with validation in simulated robotics tasks.

Findings

Algorithm achieves bounded dynamic regret.

Successfully controls inverted pendulum under disturbances.

Enables quadrotor navigation in cluttered environments.

Abstract

We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety constraints that take the form of time-varying convex constraints such as collision-avoidance and control-effort constraints. We provide an algorithm with bounded dynamic regret, i.e., bounded suboptimality against an optimal clairvoyant controller that knows the realization of the noise a prior. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite real-world unpredictable disturbances such as wind gusts. To develop the algorithm, we capture our problem as a sequential game between a controller and an adversary, where the controller plays first, choosing the control input, whereas the adversary plays second, choosing the noise's realization. The controller aims to minimize its cumulative tracking error despite being unable to know the noise's realization a prior. We validate our algorithm in simulated scenarios of (i) an inverted pendulum aiming to stay upright, and (ii) a quadrotor aiming to fly to a goal location through an unknown cluttered environment.