### Jorge Cortés

#### Professor

Universal formula for smooth safe stabilization

P. Ong, J. Cortés

Proceedings of the IEEE Conference on Decision and Control, Nice, France, 2019,
pp. 2373-2378

### Abstract

This paper formulates a safe and stabilizing control state feedback law for a control affine nonlinear system. We assume that there exist a known control Lyapunov function (CLF) and a control barrier function (CBF) that are compatible, i.e., there exists a control choice satisfying the conditions given by both the CLF and CBF at each given state. In contrast to the approach in the literature of finding a minimum-norm control using optimization on the feasible control set, we take a different approach by finding and combining different weighted centroids of the feasible control set. As a result, we can propose a control feedback law with guaranteed smoothness everywhere except at the origin, and with guaranteed continuity at the origin if small control property holds.

Mechanical and Aerospace Engineering,
University of California, San Diego

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