Chaos enhanced differential evolution in the task of evolutionary control of discrete chaotic LOZI map

In this paper, evolutionary technique Differential Evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of selected discrete chaotic system, which is the two-dimensional Lozi map. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used within Chaos enhanced heuristic concept as the chaotic pseudo-random number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudo-random sequences given by chaotic map to help Differential evolution algorithm in searching for the best controller settings for the same chaotic system. The optimizations were performed for three different required final behavior of the chaotic system, and two types of developed cost function. To confirm the robustness of presented approach, comparisons with canonical DE strategy and PSO algorithm have been performed.

[1]  Ivan Zelinka,et al.  AETA 2013: Recent Advances in Electrical Engineering and Related Sciences , 2014 .

[2]  Roman Senkerik,et al.  Investigation on evolutionary optimization of chaos control , 2009 .

[3]  Roman Senkerik,et al.  Chaos driven evolutionary algorithms for the task of PID control , 2010, Comput. Math. Appl..

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

[5]  Roman Senkerik,et al.  Scheduling the Lot-Streaming Flowshop scheduling problem with setup time with the chaos-induced Enhanced Differential Evolution , 2013, 2013 IEEE Symposium on Differential Evolution (SDE).

[6]  Arthur C. Sanderson,et al.  Adaptive Multi-objective Differential Evolution , 2009 .

[7]  Hassan Salarieh,et al.  Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty , 2012 .

[8]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[9]  Mehmet Karaköse,et al.  Chaotic-based hybrid negative selection algorithm and its applications in fault and anomaly detection , 2010, Expert Syst. Appl..

[10]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[11]  Aria Alasty,et al.  Multi-variable control of chaos using PSO-based minimum entropy control , 2011 .

[12]  Jinung An,et al.  An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization , 2013, TheScientificWorldJournal.

[13]  Leandro dos Santos Coelho,et al.  Chaotic synchronization using PID control combined with population based incremental learning algorithm , 2010, Expert Syst. Appl..

[14]  Luigi Fortuna,et al.  Chaotic sequences to improve the performance of evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[15]  Roman Senkerik,et al.  Chaos driven Differential Evolution in the task of chaos control optimization , 2010, IEEE Congress on Evolutionary Computation.

[16]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[17]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[18]  Michal Pluhacek,et al.  Utilization of analytic programming for the evolutionary synthesis of the robust multi-chaotic controller for selected sets of discrete chaotic systems , 2014, Soft Computing.

[19]  R. Vatankhah,et al.  Stabilizing chaotic system on periodic orbits using multi-interval and modern optimal control strategies , 2012 .

[20]  Roman Senkerik,et al.  Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming , 2013, Math. Comput. Model..

[21]  Donald Davendra,et al.  Traveling Salesman Problem, Theory and Applications , 2010 .

[22]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[23]  Leandro dos Santos Coelho,et al.  Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning , 2012, Comput. Math. Appl..

[24]  Michal Pluhacek,et al.  On the parameter settings for the chaotic dynamics embedded differential evolution , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[25]  L. Coelho,et al.  A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch , 2009 .

[26]  Roman Senkerik,et al.  Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation , 2010, Comput. Math. Appl..

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

[28]  J. Sprott.  Chaos and time-series analysis , 2001 .

[29]  Arthur C. Sanderson,et al.  JADE: Self-adaptive differential evolution with fast and reliable convergence performance , 2007, 2007 IEEE Congress on Evolutionary Computation.

[30]  Ivan Zelinka,et al.  Real-time deterministic chaos control by means of selected evolutionary techniques , 2009, Eng. Appl. Artif. Intell..

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

[32]  M. A. Aziz-Alaoui,et al.  Dynamics of a Hénon–Lozi-type map , 2001 .

[33]  Ivan Zelinka,et al.  Evolutionary Synchronization of Chaotic Systems , 2010, Evolutionary Algorithms and Chaotic Systems.

[34]  Michal Pluhacek,et al.  On the behavior and performance of chaos driven PSO algorithm with inertia weight , 2013, Comput. Math. Appl..

[35]  Michal Pluhacek,et al.  Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems , 2013, Comput. Math. Appl..