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Stabilization of delayed chaotic neural networks by periodically intermittent control. (English) Zbl 1170.93370
Summary: 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.
MSC:
93D21Adaptive or robust stabilization
93C15Control systems governed by ODE
92B20General theory of neural networks (mathematical biology)
References:
[1]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) · doi:10.1103/PhysRevE.50.3410
[2]T.W. Carr, I.B. Schwartz, Controlling the unstable steady state in a multimode laser. Phys. Rev. E 51(5), 5109–5111 (1995) · doi:10.1103/PhysRevE.51.5109
[3]T.W. Carr, I.B. Schwartz, Controlling high-dimensional unstable steady states using delay, duration and feedback. Physica D 96, 1–25 (1996) · Zbl 1194.93068 · doi:10.1016/0167-2789(96)00011-5
[4]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) · Zbl 1152.93488 · doi:10.1016/j.chaos.2006.05.009
[5]D. Dai, X. Ma, Chaos synchronization by using intermittent parametric adaptive control method. Phys. Lett. A 288, 23–28 (2001) · Zbl 0971.37043 · doi:10.1016/S0375-9601(01)00521-7
[6]L.M. Duan, G.C. Guo, Suppressing environmental noise in quantum computation through pulse control. Phys. Lett. A 261, 139–144 (1999) · Zbl 1044.81526 · doi:10.1016/S0375-9601(99)00592-7
[7]Z.H. Guan, G. Chen, On delayed impulsive Hopfield neural networks. Neural Netw. 12, 273–280 (1999) · doi:10.1016/S0893-6080(98)00133-6
[8]A. Halanay, Differential Equations: Stability, Oscillations, Time Lags (Academic Press, San Diego, 1966)
[9]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) · doi:10.1109/TCSII.2007.903205
[10]C.D. Li, X.F. Liao, T.W. Huang, Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17, 013103 (2007) · Zbl 1159.93353 · doi:10.1063/1.2430394
[11]H.T. Lu, Chaotic attractors in delayed neural networks. Phys. Lett. A 298, 109–116 (2002) · Zbl 0995.92004 · doi:10.1016/S0375-9601(02)00538-8
[12]T.L. Montgomery, J.W. Frey, W.B. Norris, Intermittent control systems. Environ. Sci. Technol. 9(6), 528–532 (1975) · doi:10.1021/es60104a608
[13]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) · Zbl 0956.68133 · doi:10.1109/81.802844
[14]J. Starrett, Control of chaos by occasional bang-bang. Phys. Rev. E 67, 036203 (2003) · doi:10.1103/PhysRevE.67.036203
[15]J. Sun, Delay-dependent stabilization criteria for time-delay chaotic systems via time-delay feedback control. Chaos, Solitons Fractals 21(2), 143–150 (2004) · Zbl 1048.37509 · doi:10.1016/j.chaos.2003.10.018
[16]L. Viola, S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733 (1998) · doi:10.1103/PhysRevA.58.2733
[17]L. Viola, E. Knill, S. Lloyd, Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417 (1999) · Zbl 1042.81524 · doi:10.1103/PhysRevLett.82.2417
[18]T. Yang, Impulsive Systems and Control: Theory and Application (Nova Science Publishers, New York, 2001)
[19]P. Zanardi, Symmetrizing evolutions. Phys. Lett. A 258, 77–82 (1999) · Zbl 0934.81003 · doi:10.1016/S0375-9601(99)00365-5
[20]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) · Zbl 1138.81370 · doi:10.1016/j.physleta.2004.05.019
[21]M. Zochowski, Intermittent dynamical control. Physica D 145, 181–190 (2000) · doi:10.1016/S0167-2789(00)00112-3