Observer-based Optimal Control for a Class of Impulsive Switched Systems

Optimal switch-time control is the study that investigates how best to switch between different modes. In this paper, we solve an optimal switch-time control problem for a class of impulsive switched systems based on observer design. The considered system undergoes jumps at the switching times and the state is only partially known through the outputs. The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes. We present a method that both guarantees that the current control variables remain optimal as the state estimates evolve, and that can be applied to real-time applications. Moreover, the optimal impulsive control strategy can be found using some numerical gradient descent algorithms. Finally, the viability of the proposed method is illustrated through a numerical example.