Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 210)


The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors.

The chaotic system stabilization is based on time-delay auto-synchronization (TDAS, ETDAS) and proper combination with own synthesized control law. This synthesized chaotic controller is based on one or two compensator. The primary compensator generates the perturbation sequence using TDAS/ETDAS method, second one is own design using method of GE. The original design of the objective function takes inspiration from standard control theory. All tests are performed using Matlab/Simulink environment.


Logistic equation Deterministic chaos Delayed feedback control TDAS ETDAS Metaheuristic optimization HC12 Grammatical evolution 


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Brno University of TechnologyBrnoCzech Republic

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