Kernel-based Adaptive Critic Designs for Optimal Control of Nonlinear Discrete-time System

Because it is necessary to solve the nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equations or the nonlinear two-point boundary value problems, the optimal control of nonlinear system is quite difficultly. Based on adaptive dynamic programming ( ADP) and adaptive critic designs (ACDs), the optimal control of nonlinear system theory has been intensive studied. However, based on neural network, the ADP still have the problem of network structure design and learning parameters optimization. Because the kernel function can reflect the similarity among data by the form of inner product of data, the traditional linear learning algorithm can be extended to nonlinear theoretical framework by kernel function. Based on online kernel learning, the kernel-based adaptive critic designs is studied in this paper. Then, the critic of ADP is designed by using the kernel recursive least square algorithm. Thus, the realization process of the KHDP and KDHP algorithms are obtained. Finally, example and computer simulation are shown that the kernel-based ACDs can effectively solve the optimal control of nonlinear discrete-time system.