Abstract
This paper studies the exponential stabilization of delayed chaotic neural networks (DCNNs) using what is called periodically intermittent control. An exponential stability criterion for the controlled neural networks, together with its simplified version, is established by using the Lyapunov function and Halanay inequality. The feasible region of control parameters is estimated in a rigorous way. Theoretical results and numerical simulations show that the continuous-time DCNN can be stabilized by intermittent feedback control with nonzero duration.
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References
T.W. Carr, I.B. Schwartz, Controlling unstable steady states using system parameter variation and control duration. Phys. Rev. E 50(5), 3410–3415 (1994)
T.W. Carr, I.B. Schwartz, Controlling the unstable steady state in a multimode laser. Phys. Rev. E 51(5), 5109–5111 (1995)
T.W. Carr, I.B. Schwartz, Controlling high-dimensional unstable steady states using delay, duration and feedback. Physica D 96, 1–25 (1996)
B. Chen, X.P. Liu, S.C. Tong, Guaranteed cost control of time-delay chaotic systems via memoryless state feedback. Chaos, Solitons Fractals 34, 1683–1688 (2007)
D. Dai, X. Ma, Chaos synchronization by using intermittent parametric adaptive control method. Phys. Lett. A 288, 23–28 (2001)
L.M. Duan, G.C. Guo, Suppressing environmental noise in quantum computation through pulse control. Phys. Lett. A 261, 139–144 (1999)
Z.H. Guan, G. Chen, On delayed impulsive Hopfield neural networks. Neural Netw. 12, 273–280 (1999)
A. Halanay, Differential Equations: Stability, Oscillations, Time Lags (Academic Press, San Diego, 1966)
C.D. Li, G. Feng, X. Liao, Stabilization of nonlinear systems via periodically intermittent control. IEEE Trans. Circuits Syst. II: Express Briefs 54, 1019–1023 (2007)
C.D. Li, X.F. Liao, T.W. Huang, Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17, 013103 (2007)
H.T. Lu, Chaotic attractors in delayed neural networks. Phys. Lett. A 298, 109–116 (2002)
T.L. Montgomery, J.W. Frey, W.B. Norris, Intermittent control systems. Environ. Sci. Technol. 9(6), 528–532 (1975)
E.N. Sanchez, J.P. Perez, Input-to-state stability (ISS) analysis for dynamic NN. IEEE Trans. Circuits Syst. I, Regul. Pap. 46(11), 1395–1398 (1999)
J. Starrett, Control of chaos by occasional bang-bang. Phys. Rev. E 67, 036203 (2003)
J. Sun, Delay-dependent stabilization criteria for time-delay chaotic systems via time-delay feedback control. Chaos, Solitons Fractals 21(2), 143–150 (2004)
L. Viola, S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733 (1998)
L. Viola, E. Knill, S. Lloyd, Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417 (1999)
T. Yang, Impulsive Systems and Control: Theory and Application (Nova Science Publishers, New York, 2001)
P. Zanardi, Symmetrizing evolutions. Phys. Lett. A 258, 77–82 (1999)
Y. Zhang, Z.W. Zhou, G.C. Guo, Decoupling neighboring qubits in quantum computers through bang-bang pulse control. Phys. Lett. A 327, 391–396 (2004)
M. Zochowski, Intermittent dynamical control. Physica D 145, 181–190 (2000)
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The work described in this paper was partially supported by NSFC (Grant No. 60574024) and Program for New Century Excellent Talents in University of China (NCET-06-0764).
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Huang, J., Li, C. & Han, Q. Stabilization of Delayed Chaotic Neural Networks by Periodically Intermittent Control. Circuits Syst Signal Process 28, 567–579 (2009). https://doi.org/10.1007/s00034-009-9098-3
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DOI: https://doi.org/10.1007/s00034-009-9098-3