Adaptive dynamic programming for linear impulse systems

Abstract

We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming (ADP) method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pre-impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.