Optimization-Based Safe Stabilizing Feedback With Guaranteed Region of Attraction

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