Linear impulsive system optimization using adaptive dynamic programming

This paper investigates the optimal control problem for linear impulsive systems with impulsive moments fixed. Based on adaptive dynamic programming(ADP), a numerical method is proposed to iteratively solve for this optimal impulsive control. The temporal difference of the value functions is used to determine whether the optimality has been achieved. A gradient based optimization is carried on to update the controller; The optimality principle is used to update the value function. When the optimality has been achieved, the controller output converges to the optimal impulsive control satisfying the optimality conditions. The convergence proof of this impulsive ADP algorithm is presented. Results of a scalar and a multi-variable linear impulsive systems are given in the simulation section for illustrative purpose.