Stable adaptive neurocontrol for nonlinear discrete-time systems

This paper presents a novel approach in designing neural network based adaptive controllers for a class of nonlinear discrete-time systems. This type of controllers has its simplicity in parallelism to linear generalized minimum variance (GMV) controller design and efficiency to deal with complex nonlinear dynamics. A recurrent neural network is introduced as a bridge to compensation simplify controller design procedure and efficiently to deal with nonlinearity. The network weight adaptation law is derived from Lyapunov stability analysis and the connection between convergence of the network weight and the reconstruction error of the network is established. A theorem is presented for the conditions of the stability of the closed-loop systems. Two simulation examples are provided to demonstrate the efficiency of the approach.