Optimal impulsive control of delay systems based on partial information

In this paper, the optimal impulsive control problem for a class of switched autonomous system with time-delay is studied. The considered system jumps at the switching times and the state is only partially known through the outputs. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. A method is presented that guarantees that the current switch time remains optimal as the state estimates evolve, and can be applied to real-time applications. The optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.