Virtual Target-Oriented Neural Learning for Robust Optimal Tracking Control of Discrete Strict-Feedback Systems

This article proposes a hierarchical neural learning (HNL) algorithm for optimal tracking control (OTC) of nonlinear strict-feedback systems (SFSs) with unmatched disturbances (uMDs) and unknown dynamics. Leveraging the recursive structure of SFSs, we introduce the virtual target (VT) construction scheme in which each VT is a nonlinear mapping of the current state and desired output, thereby eliminating the noncausal that typically plagues discrete-time SFS control. The VTs serve as auxiliary inputs for low-order subsystems, while a time-varying affine Hamilton-Jacobi-Isaacs (HJI) formulation establishes an explicit relationship between the auxiliary control and the disturbance. The controller is synthesized directly from input-output data, removing the need for an accurate plant model. Within an adaptive dynamic programming (ADP) framework, we further enhance the neural architecture by replacing the conventional action network with a tracking network (T-network) whose energy function merges gradient information with future tracking errors, ensuring that each policy update simultaneously reduces control effort and improves tracking accuracy. Simulations confirm that the proposed HNL scheme achieves outstanding performance in both (optimal) tracking modes, exhibiting strong robustness to uMDs and significant model uncertainties.