Optimization-Based Safe Stabilizing Feedback with Guaranteed Region of Attraction

TL;DR

This paper introduces an optimization-based feedback design framework that ensures safe stabilization of control affine systems, providing guarantees on the region of attraction and safety, with practical simulation validation.

Contribution

It presents a novel penalty-based control design method that guarantees safety and stability, extending to the entire safe set and offering inner region of attraction estimates.

Findings

Guarantees safe stabilization with a region of attraction.

Eliminates undesired equilibria through penalty parameter tuning.

Provides simulation results validating the theoretical guarantees.

Abstract

This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function (CBF) defining affine-in-the-input inequalities that certify, respectively, the stability and safety objectives for the dynamics. Leveraging ideas from penalty methods for constrained optimization, the proposed design framework imposes one of the inequalities as a hard constraint and the other one as a soft constraint. We study the properties of the closed-loop system under the resulting feedback controller and identify conditions on the penalty parameter to eliminate undesired equilibria that might arise. Going beyond the local stability guarantees available in the literature, we are able to provide an inner approximation of the region of attraction of the equilibrium, and identify conditions under which the whole safe set belongs to it. Simulations illustrate our results.