Robust decentralized adaptive control for a class of uncertain neural networks with time-varying delays

This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller.

[1]  Chih-Chiang Cheng,et al.  A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems , 2003, IEEE Trans. Autom. Control..

[2]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Bor-Sen Chen,et al.  Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach , 1991 .

[4]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[6]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[7]  Kou-Cheng Hsu Decentralized Sliding Mode Control for Large-Scale Time-Delayed Systems With Series Nonlinearities , 1999 .

[8]  D. Siljak,et al.  Robust stability and stabilization of discrete-time non-linear systems: The LMI approach , 2001 .

[9]  Sarah K. Spurgeon,et al.  Sliding Mode Control , 1998 .

[11]  Ju H. Park,et al.  Robust Nonfragile Decentralized Controller Design for Uncertain Large-Scale Interconnected Systems With Time-Delays , 2002 .

[12]  Zhenyuan Guo,et al.  Dynamical behavior of delayed Hopfield neural networks with discontinuous activations , 2009 .

[13]  Chao-Jung Cheng,et al.  Robust control of a class of neural networks with bounded uncertainties and time-varying delays , 2008, Comput. Math. Appl..

[14]  Jinde Cao,et al.  Robust Adaptive Control of Unknown Modified Cohen–Grossberg Neural Networks With Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Lihong Huang,et al.  Global Output Convergence of a Class of Recurrent Delayed Neural Networks with Discontinuous Neuron Activations , 2009, Neural Processing Letters.

[16]  Jinde Cao Global stability conditions for delayed CNNs , 2001 .

[17]  Shankar P. Bhattacharyya,et al.  On the synthesis of controllers for a non-overshooting step response , 2003, IEEE Trans. Autom. Control..

[18]  T. Liao,et al.  Globally exponential stability condition of a class of neural networks with time-varying delays , 2005 .

[19]  Ju H. Park,et al.  Decentralized dynamic output feedback controller design for guaranteed cost stabilization of large-scale discrete-delay systems , 2004, Appl. Math. Comput..

[20]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[21]  Ju H. Park Robust Decentralized Stabilization of Uncertain Large-Scale Discrete-Time Systems with Delays , 2002 .

[22]  Sabri Arik,et al.  Global stability of a class of neural networks with time-varying delay , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Wenwu Yu,et al.  Robust control of delayed Cohen–Grossberg neural networks , 2008 .

[24]  T. Liao,et al.  Globally exponential stability of generalized Cohen–Grossberg neural networks with delays , 2003 .