Dynamic Output Feedback Stabilization for Nonlinear Systems Based on Standard Neural Network Models

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.

[1]  J. Si,et al.  Neural network-based control design: an LMI approach , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[2]  Meiqin Liu,et al.  A neural network model and its application , 2004, SMC.

[3]  Panos J. Antsaklis,et al.  Neural networks for control systems , 1990, IEEE Trans. Neural Networks.

[4]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5]  Johan A. K. Suykens,et al.  Artificial Neural Networks for Modeling and Control of Non-Linear Systems , 1995 .

[6]  Kazuo Tanaka,et al.  An approach to stability criteria of neural-network control systems , 1996, IEEE Trans. Neural Networks.

[7]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[8]  Ernesto Rios-Patron,et al.  A General Framework for the Control of Nonlinear Systems , 2000 .

[9]  Peter J. Gawthrop,et al.  Neural networks for control systems - A survey , 1992, Autom..

[10]  J. Suykens,et al.  Nonlinear system identification using neural state space models, applicable to robust control design , 1995 .

[11]  R.D. Braatz,et al.  Robust nonlinear control of a pH neutralization process , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[12]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[13]  Johan A. K. Suykens,et al.  Neural networks for control , 1996 .

[14]  Tsai-Yuan Lin,et al.  An H∞ design approach for neural net-based control schemes , 2001, IEEE Trans. Autom. Control..

[15]  B. Anderson,et al.  A generalization of the Popov criterion , 1968 .

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