Online adaptive dynamic programming algorithm for linear fixed-time impulse hybrid systems

This paper studies an online adaptive dynamic programming (ADP) algorithm for linear fixed-time impulse systems. The ADP algorithm follows the value iteration method, updating the value approximation and the control law iteratively. In the algorithm, a single network structure is adopted. The single critic network approximates the objective value function. Online training of the value function and the control laws are implemented at each iteration. The network approximated value function converges to the optimal one of the impulse system. Simulations are also presented for the validity of the presented algorithm.