OPTIMAL CONTROL OF STATE-DEPENDENT IMPULSE SYSTEMS
We study an optimal control problem for a measure-driven dynamic system, where jumps of a state trajectory may occur only at the moments of hitting a given set. The model can be described by using the complementarity formalism. The system is not assumed to satisfy correctness conditions. A time reparameterization technique is developed to reduce the optimization problem to the one with bounded controls. Necessary conditions for optimality are obtained by interpreting the Maximum Principle in the reduced problem.