Newton-Geodesic HMP algorithms for the optimization of hybrid systems and the geometric properties of hybrid value functions

This paper provides algorithms for the optimization of autonomous hybrid systems based on the geometrical properties of switching manifolds. The first and second sections of the paper introduce optimal hybrid control systems and the third section presents the Newton-Geodesic-Hybrid Minimum Principle (HMP) which is an extension of the Gradient Geodesic-HMP algorithm in [4]. In the fourth section, we extend the analysis yielding the Newton-Geodesic-HMP algorithm to relate the difference of the curvatures of the ambient and switching manifolds to second order variations of the hybrid value function. Finally an example is given to illustrate the results.