Tracking control of discrete-time affine nonlinear systems based on kernel-HDP algorithm

In the past decade, adaptive dynamic programming (ADP) has been widely used to realize online learning tracking control of dynamical systems, where neural networks with manually designed features are commonly used. In order to improve the generalization capability and learning efficiency of ADP, this paper presents a novel framework of ADP with sparse kernel machines by integrating kernel methods and approximately linear dependence (ALD) analysis into the critic module of ADP for the optimal tracking controller design. An ADP algorithm based on sparse kernel learning and heuristic dynamic programming (HDP) is proposed, that is, kernel HDP (KHDP). Based on KHDP, an experiment is established. By simulation, the effectiveness of proposed algorithm is demonstrated.