Recurrent neural networks for nonlinear output regulation

Based on a power-series approximation method, recurrent neural networks (RNN) are proposed for real-time synthesis and auto-tuning of feedback controllers for nonlinear output regulation systems. The proposed neurocontrol approach represents a novel application of recurrent neural networks to the nonlinear output regulation problem. The proposed approach completely inherits the stability and asymptotic tracking properties guaranteed by original nonlinear output regulation systems, due to its globally exponential convergence. Excellent operating characteristics of the proposed RNN-based controller and the closed-loop nonlinear control systems are demonstrated by using simulation results of the ball-and-beam system and the inverted pendulum on a cart system.

[1]  Chen-Chung Liu,et al.  Adaptively controlling nonlinear continuous-time systems using multilayer neural networks , 1994, IEEE Trans. Autom. Control..

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

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

[4]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[5]  Jerry M. Mendel,et al.  Three-dimensional structured networks for matrix equation solving , 1991, Neural Networks for Signal Processing Proceedings of the 1991 IEEE Workshop.

[6]  Kumpati S. Narendra,et al.  Control of nonlinear dynamical systems using neural networks: controllability and stabilization , 1993, IEEE Trans. Neural Networks.

[7]  A. Cichocki,et al.  Neural networks for solving systems of linear equations and related problems , 1992 .

[8]  W. Rugh,et al.  An approximation method for the nonlinear servomechanism problem , 1992 .

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

[10]  W. Rugh,et al.  Stabilization on zero-error manifolds and the nonlinear servomechanism problem , 1992 .

[11]  George A. Rovithakis.  Robust neural adaptive stabilization of unknown systems with measurement noise , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Petros A. Ioannou,et al.  Linear Time-Varying Systems: Control and Adaptation , 1992 .

[13]  Allon Guez,et al.  ART based adaptive pole placement for neurocontrollers , 1991, Neural Networks.

[14]  S. Sanders,et al.  Controlling Non-Minimum Phase Nonlinear Systems - The Inverted Pendulum on a Cart Example , 1993, 1993 American Control Conference.

[15]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[16]  Jun Wang,et al.  Recurrent neural networks for solving linear inequalities and equations , 1999 .

[17]  Jun Wang,et al.  A multilayer recurrent neural network for on-line synthesis of minimum-norm linear feedback control systems via pole assignment , 1996, Autom..

[18]  Manolis A. Christodoulou,et al.  Adaptive Control with Recurrent High-order Neural Networks , 2000, Advances in Industrial Control.

[19]  P. Kokotovic,et al.  Nonlinear control via approximate input-output linearization: the ball and beam example , 1992 .

[20]  S. Bhattacharyya,et al.  Pole assignment via Sylvester's equation , 1982 .

[21]  Jun Wang,et al.  Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices , 1997, SIAM J. Sci. Comput..

[22]  Jun Wang.  Recurrent neural networks for solving linear matrix equations , 1993 .

[23]  Jie Huang,et al.  A neural-network method for the nonlinear servomechanism problem , 1999, IEEE Trans. Neural Networks.