Model-free chaos control in a chaotic Henon-like system using Takens embedding theory

In this paper, the problem of chaos control in a chaotic Henon-like system without using the governing equations of the system is investigated. It is also assumed that the system has only one measurable state. The time-series of the measurable state is used to stabilize chaos by a three-step method. First, using Takens embedding theory, a delayed phase space is reconstructed preserving the topological characteristics of the system. Then, an appropriate dynamic model is identified to estimate the time-series data in the reconstructed phase space. Finally, the unstable fixed point of the system is stabilized using an appropriate linear delayed feedback controller with controller gains systematically computed.

[1]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[2]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[3]  Hassan Salarieh,et al.  Chaos control in delayed phase space constructed by the Takens embedding theory , 2018, Commun. Nonlinear Sci. Numer. Simul..

[4]  Floris Takens,et al.  Chapter 7 – Reconstruction Theory and Nonlinear Time Series Analysis , 2010 .

[5]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[6]  De-Shuang Huang,et al.  Determining the centers of radial basis probabilistic neural networks by recursive orthogonal least square algorithms , 2005, Appl. Math. Comput..

[7]  James C. Robinson.  A topological delay embedding theorem for infinite-dimensional dynamical systems , 2005 .

[8]  Sara Dadras,et al.  Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ , 2013 .

[9]  Aria Alasty,et al.  Nonlinear feedback control of chaotic pendulum in presence of saturation effect , 2007 .

[10]  Li-Wei Ko,et al.  Adaptive synchronization of chaotic systems with unknown parameters via new backstepping strategy , 2012, Nonlinear Dynamics.

[11]  A. Mees,et al.  On selecting models for nonlinear time series , 1995 .

[12]  Frédéric Bouchara,et al.  Influence of noise on the averaged false neighbors method for analyzing time series , 2006 .

[13]  Jan Swevers,et al.  Identification of nonlinear systems using Polynomial Nonlinear State Space models , 2010, Autom..

[14]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .