Semidefinite programming approaches to multi-contact feedback control

Abstract

We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We examine several different models of such systems and the roles of semidefinite programming and sums-of-squares programming in designing and verifying stabilizing controllers. First the system is modelled as a discrete-time piecewise affine system and we use semidefinite programming to design stabilizing controllers according to Lyapunov theory. Second the system is modelled as a discrete-time piecewise polynomial system and we use sums-of-squares programming to design feedback controllers. Third the system is modelled as a discrete-time polynomial system with linear complimentarity constraints for contacts and we use sums-of-squares to verify the controllers according to Lyapunov theory.