Control Synthesis for Stability and Safety by Differential Complementarity Problem

This paper develops a novel control synthesis method for safe stabilization of control-affine systems as Differential Complementarity Problem (DCP). Our design uses Lyapunov function (CLF) and barrier (CBF) to define complementarity constraints in the DCP formulation certify stability safety, respectively. The CLF-CBF-DCP controller imposes soft constraint, which is automatically relaxed when safety constraint active, without need parameter tuning or optimization. We study closed-loop system behavior with identify conditions on existence local equilibria. Although certain cases yields undesirable equilibria, those can be confined small subset set boundary by proper choice parameters. Then, our avoid equilibria that CLF-CBF quadratic programming techniques encounter.