Multiobjective synchronization of coupled systems.

In this paper, multiobjective synchronization of chaotic systems is investigated by especially simultaneously minimizing optimization of control cost and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach that includes a hybrid chromosome representation. The hybrid encoding scheme combines binary representation with real number representation. The constraints on the coupling form are also considered by converting the multiobjective synchronization into a multiobjective constraint problem. In addition, the performances of the adaptive learning method and non-dominated sorting genetic algorithm-II as well as the effectiveness and contributions of the proposed approach are analyzed and validated through the Rössler system in a chaotic or hyperchaotic regime and delayed chaotic neural networks.

[1]  Francesco Sorrentino.  Adaptive coupling for achieving stable synchronization of chaos. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alexander L. Fradkov,et al.  Controlled synchronization under information constraints. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[4]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[5]  Anil K. Jain,et al.  Dimensionality reduction using genetic algorithms , 2000, IEEE Trans. Evol. Comput..

[6]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[7]  Parlitz,et al.  Estimating model parameters from time series by autosynchronization. , 1996, Physical review letters.

[8]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[9]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[10]  M. A. Muñoz,et al.  Entangled networks, synchronization, and optimal network topology. , 2005, Physical review letters.

[11]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[12]  Runhe Qiu,et al.  Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays☆ , 2008 .

[13]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[14]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[15]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Kay Chen Tan,et al.  Hybrid Multiobjective Evolutionary Design for Artificial Neural Networks , 2008, IEEE Transactions on Neural Networks.

[18]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[19]  O. Rössler.  An equation for hyperchaos , 1979 .

[20]  Zidong Wang,et al.  Pinning control of fractional-order weighted complex networks. , 2009, Chaos.

[21]  Alexander L. Fradkov,et al.  Introduction to Control of Oscillations and Chaos , 1998 .

[22]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[23]  Adilson E Motter,et al.  Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions , 2009, Proceedings of the National Academy of Sciences.

[24]  E. Ott.  Chaos in Dynamical Systems: Contents , 2002 .

[25]  Antonio Loría,et al.  A Linear Time-Varying Controller for Synchronization of LÜ Chaotic Systems With One Input , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[27]  Debin Huang,et al.  Stabilizing near-nonhyperbolic chaotic systems with applications. , 2004, Physical review letters.

[28]  Renato A. Krohling,et al.  Design of optimal disturbance rejection PID controllers using genetic algorithms , 2001, IEEE Trans. Evol. Comput..

[29]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[30]  Henry D I Abarbanel,et al.  Parameter and state estimation of experimental chaotic systems using synchronization. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[32]  Henk Nijmeijer,et al.  A dynamical control view on synchronization , 2001 .

[33]  Ilʹi︠a︡ Izrailevich Blekhman,et al.  Synchronization in science and technology , 1988 .

[34]  Changsong Zhou,et al.  Universality in the synchronization of weighted random networks. , 2006, Physical review letters.

[35]  F. Garofalo,et al.  Synchronization of complex networks through local adaptive coupling. , 2008, Chaos.

[36]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  O. Rössler.  An equation for continuous chaos , 1976 .

[38]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[39]  E. Ott,et al.  Adaptive synchronization of coupled chaotic oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  J. Rogers.  Chaos , 1876 .

[41]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

[42]  Khaled Ghédira,et al.  The r-Dominance: A New Dominance Relation for Interactive Evolutionary Multicriteria Decision Making , 2010, IEEE Transactions on Evolutionary Computation.