Guard synthesis for safety of hybrid systems using sum of squares programming

S. Coogan, M. Arcak
Proceedings of the 51st IEEE Conference on Decision and Control, 2012


We present a technique for synthesizing switching guards for hybrid systems by using sum of squares (SOS) programming. The guards are defined to be semialgebraic sets calculated from a bilinear SOS program. We present a method for ensuring that synthesized guards satisfy a state-based safety constraint and do not allow Zeno executions. We use an iterative algorithm to solve the bilinear program and demonstrate our approach with an example.