Dynamic learning from neural network‐based control for sampled‐data strict‐feedback nonlinear systems

Abstract

AbstractThis article focuses on the dynamic learning and control problem for a class of nonlinear sampled‐data systems in strict‐feedback form. To achieve learning of unknown system dynamics in closed‐loop control, two obstacles need to be overcome: the inherent noncausal problem in the backstepping design of discrete‐time nonlinear systems, and the exponential stability of the sampling closed‐loop error system. First, a novel command filtered adaptive neural control is developed to achieve closed‐loop stability and the convergence of output tracking error based on Lyapunov theory, the noncausal problem is overcome by utilizing the command filter technique, and the ‐step delay is avoided in the recursive process. Second, by combining a state transformation method, the closed‐loop error system is divided into perturbed linear time‐varying (LTV) subsystems. Based on the convergence of the tracking errors, the partial persistent excitation (PE) condition of the radial basis function network is verified and established recursively. By extending the exponential stability result of a class of discrete‐time LTV systems, the convergence of the estimated weights to their optimal values is guaranteed with the PE condition. Subsequently, locally accurate approximation/learning of the unknown closed‐loop sampled dynamics can be obtained and stored in the form of constant neural networks. Finally, by reutilizing the acquired knowledge, a learning‐based control scheme for the sampled‐data system is further proposed to pursue improved control performance. Simulation studies are performed to illustrate the validity of the proposed scheme.