Tracking control of affine nonlinear discrete-time systems based on Gaussian-kernel-based ADP

Abstract

Due to the inherent nonlinearity of Hamilton-Jacobi-Bellman (HJB) equations for the optimal control of general affine nonlinear discrete-systems, it is difficult to obtain the analytic solutions of optimal tracking control of nonlinear systems, adaptive dynamic programming (ADP) with critic-actor architecture provides an effective way to realize online learning tracking control of dynamical systems. Neural networks based ADP algorithms with empirical design of critic networks often suffer into the local minima in neural network training. To overcome the difficulty of designing model structure in parametric models and improve the generalization capability of ADP, a two-phase value iteration method for a Gaussian-kernel-based critic network is presented. It is able to update the hyper-parameter of the kernel function and the values of samples simultaneously. Combining this critic network design with actor network, the Gaussian-kernel-based adaptive dynamic programming (GK-ADP) approach for trace tracking is proposed. By simulation, the effectiveness of the GK-ADP for tracking control of discrete-time affine nonlinear systems is verified.