Gradient-geodesic HMP algorithms for the optimization of Hybrid systems based on the geometry of switching manifolds

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 deals with the analysis of the Hybrid Maximum Principle (HMP) algorithm introduced in. The HMP algorithm in is then extended to a geometrical algorithm by employing the notion of geodesic curves on switching manifolds. The convergence analysis for the proposed algorithm is based on Lasalle Theory. To reduce the computational burden, a simplified version of the geodesic algorithm is formulated in the local coordinate system of the switching state. Simulation results show a significant improvement in terms of convergence rate and stability compared with the HMP algorithm.