Optimal control for singularly impulsive dynamical systems

Singularly impulsive (or generalized impulsive) dynamical systems are systems with dynamics that are characterized by the set of differential, difference and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. For the class of singularly impulsive dynamical systems we present optimal control results. We developed unified framework for hybrid feedback optimal and inverse optimal control involving a hybrid nonlinear-nonquadratic performance functional. It is shown that the hybrid cost functional can be evaluated in closed-form as long as the cost functional considered is related in a specific way to an underlying Lyapunov function that guarantees asymptotic stability of the nonlinear closed-loop singularly impulsive system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, hybrid Hamilton-Jacobi-Bellman equation.