Numerical integration of hybrid dynamical systems via domain relaxation

Though hybrid dynamical systems are a powerful modeling tool, it has proven difficult to accurately simulate their trajectories. In this paper, we develop a provably convergent numerical integration scheme for approximating trajectories of hybrid dynamical systems. This is accomplished by first relaxing hybrid systems whose continuous states reside on manifolds by attaching epsilon-sized strips to portions of the boundary and then extending the dynamic and distance metric onto these strips. On this space we develop a numerical integration scheme and prove that discrete approximations converge to trajectories of the hybrid system. An example is included to illustrate the approach.