An error analysis for execution traces of hybrid automata using Jacobi’s equation

We present an error analysis for execution traces of hybrid automata. We describe an interpretation of Jacobi’s variational equation as the infinitesimal separation between geodesics in the plant state space. This allows us to estimate the distance between the plant state evolution produced by a hybrid control automata and geodesic curves with respect to some Lagrangian cost function. We provide an analysis for both control automata extracted from convex problems and chattering controllers extracted from measure valued control laws.