Optimal Controls for a Class of Impulsive Systems with Hybrid Quadratic Performance

In this paper we derived the necessary and sufficient conditions of optimal controls for impulsive systems with hybrid quadratic criterion. The linear time-variant systems we consider have impulsive at some fixed time. We find both open-loop and closed-loop optimal controls. By the solution of impulsive Riccati equation, we find expressions for optimal control, optimal trajectory and optimal value.