Design Of Advanced Targeting Cost Function For Evolutionary Optimization Of Chaos Control

This research deals with the optimization of the control of chaos by means of evolutionary algorithms. The main aim of this work is to show that powerful optimizing tools like evolutionary algorithms can in reality be used for the optimization of deterministic chaos control. This work is aimed on an explanation of how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing very fast and precise stabilization of desired state for any initial conditions. As a model of deterministic chaotic system, the two dimensional Henon map was used. The evolutionary algorithm SelfOrganizing Migrating Algorithm (SOMA) was used in four versions. For each version, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF.

[1]  Kestutis Pyragas.  Control of chaos via extended delay feedback , 1995 .

[2]  M. R. Irving,et al.  Observability Determination in Power System State Estimation Using a Network Flow Technique , 1986, IEEE Transactions on Power Systems.

[3]  John Starrett.  Time-optimal chaos control by center manifold targeting. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Andrzej Bargiela,et al.  Fuzzy fractal dimensions and fuzzy modeling , 2003, Inf. Sci..

[5]  Ramakrishna Ramaswamy,et al.  TARGETING CHAOS THROUGH ADAPTIVE CONTROL , 1998, chao-dyn/9801024.

[6]  Wolfram Just,et al.  Principles of Time Delayed Feedback Control , 2006 .

[7]  Eric J. Kostelich,et al.  Optimal targeting of chaos , 1998 .

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

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

[10]  Roman Senkerik,et al.  Design Of Targeting Cost Function For Evolutionary Optimization Of Chaos Control , 2007 .

[11]  Serdar Iplikci,et al.  An improved neural network based targeting method for chaotic dynamics , 2003 .

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

[13]  Hendrik Richter,et al.  Optimization of local control of chaos by an evolutionary algorithm , 2000 .

[14]  Hendrik Richter.  An Evolutionary Algorithm for Controlling Chaos: The Use of Multi-objective Fitness Functions , 2002, PPSN.

[15]  Roman Senkerik,et al.  OPTIMIZATION OF FEEDBACK CONTROL OF CHAOS BY EVOLUTIONARY ALGHORITHMS , 2006 .

[16]  Andrzej Bargiela,et al.  A model of granular data: a design problem with the Tchebyschev FCM , 2005, Soft Comput..

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

[18]  P. J. Aston,et al.  Targeting in the presence of noise , 1998 .

[19]  Andrzej Bargiela,et al.  Granular prototyping in fuzzy clustering , 2004, IEEE Transactions on Fuzzy Systems.

[20]  Serdar Iplikci,et al.  Control of chaotic systems using targeting by extended control regions method , 2001 .

[21]  Oh-Jong Kwon,et al.  Targeting and stabilizing chaotic trajectories in the standard map , 1999 .