Gradient geodesic and Newton geodesic HMP algorithms for the optimization of hybrid systems

This paper provides algorithms for the optimization of autonomous hybrid systems based on the geometrical properties of switching manifolds. By employing the notion of geodesic curves on switching manifolds, the Hybrid Maximum Principle (HMP) algorithm introduced in Shaikh and Caines (2007) is extended to the so-called gradient geodesic and Newton geodesic algorithms. The convergence analysis for the algorithms is based upon the Lasalle Invariance Principle and simulation results illustrate their efficacy.