Stability analysis of dynamic neural control

Abstract In this paper, the authors summarize their research related to dynamic neural control. In particular, results on nonlinear system identification, nonlinear trajectory tracking, and input-to-state stability (ISS) of dynamic neural networks are presented. The main analysis tool utilized is the Lyapunov approach. References for the detailed demonstrations are given. We illustrate the applicability of the results by means of examples.

[1]  Pravin Varaiya,et al.  Bounded-input bounded-output stability of nonlinear time-varying differential systems. , 1966 .

[2]  M. Agarwal A systematic classification of neural-network-based control , 1997 .

[3]  Manolis A. Christodoulou,et al.  Adaptive control of unknown plants using dynamical neural networks , 1994, IEEE Trans. Syst. Man Cybern..

[4]  Alexander S. Poznyak,et al.  Nonlinear adaptive trajectory tracking using dynamic neural networks , 1999, IEEE Trans. Neural Networks.

[5]  Eduardo Sontag Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[6]  Eduardo D. Sontag,et al.  On the Input-to-State Stability Property , 1995, Eur. J. Control.

[7]  Edgar N. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[8]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[9]  J. Willems Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[10]  K. Warwick,et al.  Dynamic recurrent neural network for system identification and control , 1995 .

[11]  J. Tsinias Sontag's “input to state stability condition” and global stabilization using state detection , 1993 .

[12]  J.P. Perez,et al.  Robust adaptive nonlinear system identification and trajectory tracking by dynamic neural networks , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[13]  Alexander S. Poznyak,et al.  Nonlinear System Approximation by Neural Networks: Error Stability Analysis , 1995, Intell. Autom. Soft Comput..

[14]  Alexander S. Poznyak,et al.  Non-Linear System On-Line Identification using Dynamic Neural Networks , 1999, Intell. Autom. Soft Comput..

[15]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.