Learning from Neural Control for a Class of Discrete-Time Nonlinear Systems

In this paper, based on a recent result on deterministic learning theory, we investigate learning from adaptive neural control for a class of discrete-time nonlinear systems. First, we use an adaptive neural control law without any robustification term to ensure the finite time tracking error convergence. With the tracking convergence of the system states to a periodic reference orbit, a partial PE condition of internal states is satisfied. Secondly, by using the stability result of linear discrete time-varying systems, it will be shown that exponential stability of the weight estimation subsystem along the tracking orbit is achieved, and convergence of certain neural weights of the neurons centered along the tracking orbit to their optimal values is guaranteed. Thus, locally-accurate NN approximation of the unknown dynamics is achieved by constant RBF networks. A neural learning control scheme is also presented in which the learned knowledge stored in constant RBF networks is embedded, and good tracking performance is achieve without further adaptation of neural weights. Simulation studies are included to demonstrate the effectiveness of the proposed approach.