On the Geometry of Switching Manifolds for Autonomous Hybrid Systems

This paper provides a geometrical analysis of autonomous hybrid systems optimal control (HSOC) by studying the properties of optimal hybrid system trajectories and the manifolds on which they switch between controlled vector fields. First, results previously obtained in Taringoo and Caines [2009a], Taringoo and Caines [2009c] on the parameter optimization of switching manifolds are reviewed. Second, we analyse (i) the geometric properties of switching manifolds and (ii) the sensitivities of optimal control trajectories and their connections with the Hessians of the value function of hybrid optimal control problems (HOCP).