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.

[1]  Frank L. Lewis,et al.  Multilayer discrete-time neural-net controller with guaranteed performance , 1996, IEEE Trans. Neural Networks.

[2]  Cong Wang,et al.  Deterministic learning of nonlinear dynamical systems , 2003, Proceedings of the 2003 IEEE International Symposium on Intelligent Control.

[3]  Marios M. Polycarpou,et al.  Modelling, Identification and Stable Adaptive Control of Continuous-Time Nonlinear Dynamical Systems Using Neural Networks , 1992, 1992 American Control Conference.

[4]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[5]  K S Narendra,et al.  IDENTIFICATION AND CONTROL OF DYNAMIC SYSTEMS USING NEURAL NETWORKS , 1990 .

[6]  Marios M. Polycarpou,et al.  Stable adaptive neural control scheme for nonlinear systems , 1996, IEEE Trans. Autom. Control..

[7]  Cong Wang,et al.  Deterministic Learning and Rapid Dynamical Pattern Recognition , 2007, IEEE Transactions on Neural Networks.

[8]  F. Lewis,et al.  Discrete-time neural net controller for a class of nonlinear dynamical systems , 1996, IEEE Trans. Autom. Control..

[9]  Shuzhi Sam Ge,et al.  Direct adaptive NN control of a class of nonlinear systems , 2002, IEEE Trans. Neural Networks.

[10]  F. J. Narcowich,et al.  Persistency of Excitation in Identification Using Radial Basis Function Approximants , 1995 .

[11]  Dimitry M. Gorinevsky,et al.  On the persistency of excitation in radial basis function network identification of nonlinear systems , 1995, IEEE Trans. Neural Networks.

[12]  Nader Sadegh,et al.  A perceptron network for functional identification and control of nonlinear systems , 1993, IEEE Trans. Neural Networks.

[13]  Frank L. Lewis,et al.  Discrete-time neural net controller with guaranteed performance , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[15]  Shuzhi Sam Ge,et al.  Adaptive NN control for a class of discrete-time nonlinear systems based on input-output model , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[16]  Jay A. Farrell,et al.  Stability and approximator convergence in nonparametric nonlinear adaptive control , 1998, IEEE Trans. Neural Networks.

[17]  Fu-Chuang Chen,et al.  Adaptive control of nonlinear systems using neural networks , 1992 .

[18]  Cong Wang,et al.  Learning from neural control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[19]  Songwu Lu,et al.  Robust nonlinear system identification using neural-network models , 1998, IEEE Trans. Neural Networks.

[20]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[21]  David J. Hill,et al.  Deterministic Learning Theory , 2009 .