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An improved harmony search algorithm for synchronization of discrete-time chaotic systems

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  • Santos Coelho, Leandro dos
  • de Andrade Bernert, Diego Luis

Abstract

The harmony search (HS) algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. HS was conceptualized using an analogy with music improvisation process where music players improvise the pitches of their instruments to obtain better harmony. The HS algorithm does not require initial values and uses a random search instead of a gradient search, so derivative information is unnecessary. Furthermore, the HS algorithm is simple in concept, few in parameters, easy in implementation, imposes fewer mathematical requirements, and does not require initial value settings of the decision variables. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The tuning of a proportional–integral–derivative (PID) controller based on an improved HS (IHS) algorithm for synchronization of two identical discrete chaotic systems subject the different initial conditions is investigated in this paper. Simulation results of the IHS to determine the PID parameters to synchronization of two Hénon chaotic systems are compared with other HS approaches including classical HS and global-best HS. Numerical results reveal that the proposed IHS method is a powerful search and controller design optimization tool for synchronization of chaotic systems.

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  • Santos Coelho, Leandro dos & de Andrade Bernert, Diego Luis, 2009. "An improved harmony search algorithm for synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2526-2532.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2526-2532
    DOI: 10.1016/j.chaos.2008.09.028
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    Cited by:

    1. Josephy Dias Santos & Frederico Marques & Lina Paola Garcés Negrete & Gelson A. Andrêa Brigatto & Jesús M. López-Lezama & Nicolás Muñoz-Galeano, 2022. "A Novel Solution Method for the Distribution Network Reconfiguration Problem Based on a Search Mechanism Enhancement of the Improved Harmony Search Algorithm," Energies, MDPI, vol. 15(6), pages 1-15, March.
    2. Amaya, Ivan & Cruz, Jorge & Correa, Rodrigo, 2015. "Harmony Search algorithm: a variant with Self-regulated Fretwidth," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1127-1152.
    3. Hallaji, Majid & Dideban, Abbas & Khanesar, Mojtaba Ahmadieh & kamyad, Ali vahidyan, 2018. "Optimal synchronization of non-smooth fractional order chaotic systems with uncertainty based on extension of a numerical approach in fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 325-340.

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