Control of chaotic systems using targeting by extended control regions method

In this work, the previously proposed extended control regions (ECR) algorithm for targeting is improved by using individual neural networks for each activation region. The improved version, which exploits the short time predictability of the chaotic system more efficiently, gives better performance with respect to training time and average reaching time while maintaining the advantages of the previous method. Moreover, the simulation results revealed that the meaningful number of activation regions of the controller using improved ECR is nearly linearly related with the prediction horizon of the chaotic system to be targeted, which can be used as a criterion for choosing the number of activation region.

[1]  Rollins,et al.  Controlling chaos in highly dissipative systems: A simple recursive algorithm. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Ricard V. Solé,et al.  Controlling chaos in discrete neural networks , 1995 .

[3]  Takens,et al.  Neural network model to control an experimental chaotic pendulum. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Kok Lay Teo,et al.  Directing Orbits of Chaotic Systems in the Presence of Noise: Feedback Correction , 1997 .

[5]  A. N. Sharkovskiĭ.  Dynamic systems and turbulence , 1989 .

[6]  Grebogi,et al.  Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Ding,et al.  Controlling chaos in high dimensions: Theory and experiment. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Vassilios Kovanis,et al.  Using neural networks for controlling chaos. , 1994 .

[9]  Grebogi,et al.  Controlling chaos in high dimensional systems. , 1992, Physical review letters.

[10]  Henning Lenz,et al.  Robust Control of the Chaotic Lorenz System , 1997 .

[11]  W. Ditto,et al.  Chaos: From Theory to Applications , 1992 .

[12]  Grebogi,et al.  Using the sensitive dependence of chaos (the "butterfly effect") to direct trajectories in an experimental chaotic system. , 1992, Physical review letters.

[13]  Grebogi,et al.  Using chaos to direct orbits to targets in systems describable by a one-dimensional map. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[14]  Kevin Judd,et al.  Targeting using global models built from nonstationary data , 1997 .

[15]  Keiji Konishi,et al.  Stabilizing and tracking unstable focus points in chaotic systems using a neural network , 1995 .

[16]  Kevin Judd,et al.  Creating periodic orbits in chaotic systems , 1995 .

[17]  Grebogi,et al.  Higher-dimensional targeting. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  James B. Elsner,et al.  Predicting time series using a neural network as a method of distinguishing chaos from noise , 1992 .

[19]  M. Paskota,et al.  Targeting moving targets in chaotic dynamical systems , 1997 .

[20]  Keiji Konishi,et al.  Control of chaotic systems using an on-line trained linear neural controller , 1997 .

[21]  C. M. van den Bleek,et al.  Neural networks for prediction and control of chaotic fluidized bed hydrodynamics: a first step , 1997 .

[22]  Rollins,et al.  Automated adaptive recursive control of unstable orbits in high-dimensional chaotic systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Kok Lay Teo,et al.  Directing Orbits of Chaotic Dynamical Systems , 1995 .

[24]  Visarath In,et al.  Tracking unstable periodic orbits in nonstationary high-dimensional chaotic systems:Method and experiment , 1997 .

[25]  Ute Dressler,et al.  Controlling chaotic dynamical systems using time delay coordinates , 1992 .

[26]  Eric R. Weeks,et al.  Evolving artificial neural networks to control chaotic systems , 1997 .

[27]  Kok Lay Teo,et al.  Geometry of Targeting of Chaotic Systems , 1995 .

[28]  Ott,et al.  Controlling chaos using time delay coordinates via stabilization of periodic orbits. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Grebogi,et al.  Using chaos to direct trajectories to targets. , 1990, Physical review letters.

[30]  E. Ott,et al.  Controlling Chaotic Dynamical Systems , 1991, 1991 American Control Conference.

[31]  Kok Lay Teo,et al.  Mixed Strategy Global Sub-Optimal Feedback Control for Chaotic Systems , 1997 .

[32]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[33]  Murilo S. Baptista,et al.  Targeting Applying ε-Bounded Orbit Correction Perturbations , 1998 .