zbMATH — the first resource for mathematics

Feedback control and adaptive control of the energy resource chaotic system. (English) Zbl 1129.93403
Summary: The problem of control for the energy resource chaotic system is considered. Two different method of control, feedback control (include linear feedback control, non-autonomous feedback control) and adaptive control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. The Routh-Hurwitz criteria and Lyapunov direct method are used to study the conditions of the asymptotic stability of the steady states of the controlled system. The designed adaptive controller is robust with respect to a certain class of disturbances in the energy resource chaotic system. Numerical simulations are presented to show these results.

93B52 Feedback control
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N25 Dynamical systems in biology
92B20 Neural networks for/in biological studies, artificial life and related topics
93C40 Adaptive control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D20 Asymptotic stability in control theory
Full Text: DOI
[1] Huber, A.W., Adaptive control of chaotic system, Helv acta, 62, 343-346, (1989)
[2] Ott, E.; Grebogi, C.; Yorke, J.A., Controlling chaos, Phys rev lett, 64, 1196-1199, (1990) · Zbl 0964.37501
[3] Bai, E.W.; Lonngren, K.E., Sequential synchronization of two Lorenz systems using active control, Chaos, solitons & fractals, 11, 1041-1044, (2000) · Zbl 0985.37106
[4] Yang, X.S.; Chen, G., Some observer-based criteria for discrete-time generalized chaos synchronization, Chaos, solitons & fractals, 13, 1303-1308, (2002) · Zbl 1006.93580
[5] Chen, G.; Dong, X., On feedback control of chaotic continuous time systems, IEEE trans circ syst, 40, 591, (1993) · Zbl 0800.93758
[6] Yassen, M.T., Chaos control of Chen chaotic dynamical system, Chaos, solitons & fractals, 15, 271, (2003) · Zbl 1038.37029
[7] Yassen, M.T., Controlling chaos and synchronization for new chaotic system using linear feedback, Chaos, solitons & fractals, 26, 913, (2005) · Zbl 1093.93539
[8] Agiza, H.N., Controlling chaos for the dynamical system of coupled dynamos, Chaos, solitons & fractals, 12, 341, (2002) · Zbl 0994.37047
[9] Sanchez, E.N.; Perez, J.P.; Martinez, M.; Chen, G., Chaos stabilization: an inverse optimal control approach, Latin am appl res: int J, 32, 111, (2002)
[10] Yassen, M.T., Adaptive control and synchronization of a modified chua’s circuit system, Appl math comput, 135, 113, (2001) · Zbl 1038.34041
[11] Liao, T.-L.; Lin, S.-H., Adaptive control and synchronization of Lorenz systems, J franklin inst, 336, 925, (1999) · Zbl 1051.93514
[12] Mei Sun, Lixin Tian. An energy resources demand-supply system and its dynamical analysis. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.10.085. · Zbl 1133.91524
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.