Hybrid dynamical systems have vast applications in a wide range of areas, including cyber-physical systems, power systems, mechanical and aerospace systems, etc. The hybrid systems theory has been extensively developed for systems evolving on the Euclidean space. However, many mechanical and aerospace systems evolve on more general spaces – manifolds. Many existing tools for hybrid dynamical systems do not account for this fact, and thus, are not readily applicable to the manifold setting. Therefore, to bridge this gap, the focus of this proposal is to develop tools for analysis and control of geometric hybrid dynamical systems on abstract manifolds using only the underlying topological structure of the manifold.

We propose the following five research thrusts in this proposal. Our first thrust is focused on a geometric modeling hybrid dynamical systems on manifolds. In our second thrust, we formulate topological notions of invariance, stability, attractivity, and asymptotic stability of a set. We also consider the safety problem, which is crucial in obstacle avoidance applications. In our third thrust, we present sufficient conditions to certify the geometric notions presented in the second thrust. Our fourth thrust is focused on two safety-critical optimal control applications. Finally, our fifth thrust is focused on observer-based control of rigid body attitude. 

Event Host: Piyush Jirwankar, Ph.D. Student, Electrical & Computer Engineering

Advisor: Ricardo Sanfelice