Comparison of Swarm and Evolutionary Based Algorithms for the Stabilization of Chaotic Oscillations

In this research, evolutionary based algorithm Differential Evolution (DE) is compared with swarm based optimization technique PSO in the task of optimal evolutionary tuning of controller parameters for the stabilization of nonlinear chaotic oscillations of the two-dimensional Lozi map. The novelty of the approach is that the most utilized examples of evolutionary/swarm based algorithms are compared directly on the highly nonlinear and complex multimodal optimization and simulation task. The simulations were performed for two different required final behavior of the chaotic system.

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

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

[3]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

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

[5]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

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

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

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

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

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

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

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

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

[14]  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.

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