Discrete-Time Sliding-Mode Control Based on Neural Networks

In this paper, we present a new sliding mode controller for a class of unknown nonlinear discrete-time systems. We make the following two modifications: 1) The neural identifier which is used to estimate the unknown nonlinear system, applies new learning algorithms. The stability and non-zero properties are proved by dead-zone and projection technique. 2) We propose a new sliding surface and give a necessary condition to assure exponential decrease of the sliding surface. The time-varying gain in the sliding mode produces a low-chattering control signal. The closed-loop system with sliding mode controller and neural identifier is proved to be stable by Lyapunov method.

[1]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[2]  Sarangapani Jagannathan,et al.  Control of a class of nonlinear discrete-time systems using multilayer neural networks , 2001, IEEE Trans. Neural Networks.

[3]  Quanmin Zhu,et al.  Stable adaptive neurocontrol for nonlinear discrete-time systems , 2004, IEEE Trans. Neural Networks.

[4]  S. Żak,et al.  On discrete-time variable structure sliding mode control , 1999 .

[5]  R. Fung,et al.  Comparison of sliding-mode and fuzzy neural network control for motor-toggle servomechanism , 1998 .

[6]  Daniel G. Sbarbaro-Hofer,et al.  An adaptive sliding-mode controller for discrete nonlinear systems , 2000, IEEE Trans. Ind. Electron..

[7]  Alexander S. Poznyak,et al.  Neural adaptive control of two-link manipulator with sliding mode compensation , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[8]  Heinz Unbehauen,et al.  A new algorithm for discrete-time sliding-mode control using fast output sampling feedback , 2002, IEEE Trans. Ind. Electron..

[9]  Xiaoou Li,et al.  Observer-based neuro identifier , 2000 .

[10]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[11]  Yong Fang,et al.  Use of a recurrent neural network in discrete sliding-mode control , 1999 .

[12]  H. Sira-Ramírez.  Non-linear discrete variable structure systems in quasi-sliding mode , 1991 .

[13]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[14]  Hazem N. Nounou,et al.  Stable auto-tuning of adaptive fuzzy/neural controllers for nonlinear discrete-time systems , 2004, IEEE Transactions on Fuzzy Systems.

[15]  Hung-Yuan Chung,et al.  Neuro-sliding mode control with its applications to seesaw systems , 2001, IEEE Transactions on Neural Networks.

[16]  Andrzej Bartoszewicz,et al.  Discrete-time quasi-sliding-mode control strategies , 1998, IEEE Trans. Ind. Electron..

[17]  Hassan K. Khalil,et al.  Adaptive control of a class of nonlinear discrete-time systems using neural networks , 1995, IEEE Trans. Autom. Control..