Discrete-Time Impulsive Adaptive Dynamic Programming

In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal impulsive control problems for infinite horizon discrete-time nonlinear systems. Considering the constraint of the impulsive interval, in each iteration, the iterative impulsive value function under each possible impulsive interval is obtained, and then the iterative value function and iterative control law are achieved. A new convergence analysis method is developed which proves an iterative value function to converge to the optimum as the iteration index increases to infinity. The properties of the iterative control law are analyzed, and the detailed implementation of the optimal impulsive control law is presented. Finally, two simulation examples with comparisons are given to show the effectiveness of the developed method.