Directing orbits of chaotic systems using a hybrid optimization strategy

Li, Ling-Lai; Tang, Fen

doi:10.1016/j.physleta.2004.02.026

Cited by 19 publications

(6 citation statements)

References 4 publications

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“…Directing orbits of chaotic systems is a multi-modal numerical optimization problem [8] [9]. Consider the following discrete chaotic dynamical system:…”

Section: Application To Direct Orbits Of Chaotic Systemsmentioning

confidence: 99%

Using Bat Algorithm with Levy Walk to Solve Directing Orbits of Chaotic Systems

Cai

Wang

Cui

et al. 2014

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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Abstract. Bat algorithm is a novel swarm intelligent version by simulating the bat seeking behavior. However, due to the poor exploitation, the performance is not well. Therefore, a new variant named bat algorithm with Gaussian walk is proposed in which the original uniform sample manner is replaced by one Gaussian sample. In this paper, we want to further investigate the performance with Levy sampling manner. To test its performance, three other variants of bat algorithms are employed to compare, simulation results show our modification is superior to other algorithms.

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“…Directing orbits of chaotic systems is a multi-modal numerical optimization problem [8] [9]. Consider the following discrete chaotic dynamical system:…”

Section: Application To Direct Orbits Of Chaotic Systemsmentioning

confidence: 99%

Using Bat Algorithm with Levy Walk to Solve Directing Orbits of Chaotic Systems

Cai

Wang

Cui

et al. 2014

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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“…It was regarded that chaos synchronization also can be formulated as the above problem [15,16]. Similarly, assume that feedback only acts on the first component, i.e., K 11 (k) 5 0 and all other components of K(k) are zeros.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Table 3 lists the SR and AVEN under different combination of N, l and e. From Table 3, firstly it can be concluded that PSO can direct the chaotic orbit to target region with high probability. Secondly, by comparing the results using genetic algorithm [15] and simplex-annealing strategy [16], less evaluation number is needed for PSO so that PSO is more efficient. However, as e decreases (better directing precision degree is required) it can be seen that SR decreases and AVEN increases respectively when the combination of N and l is fixed.…”

Section: Simulation On Directing Chaotic Orbitsmentioning

confidence: 99%

“…Meanwhile, it was also pointed out that chaos synchronization could be dealt with as a chaos control problem [14]. And in [15,16] algorithm and a simplex-annealing strategy were applied to such issues respectively, since essentially such class of problems can be cast as high-dimensional optimization problems from the viewpoint of optimization. Some other recent related research in this active field of research includes [17][18][19][20][21][22][23][24][25][26][27][28], etc.…”

Section: Introductionmentioning

confidence: 99%

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Directing orbits of chaotic systems by particle swarm optimization

Liu

Wang

et al. 2006

Chaos, Solitons & Fractals

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“…From the viewpoint of optimization, control of chaotic systems could be formulated as multi-modal constrained numerical optimization problems [47][48][49]. Genetic algorithm [50], simplex-annealing strategy [51], Particle swarm optimization [52], and Differential Evolution [53] have been considered. Wang et al [51] proposed an effective hybrid optimization strategy by combining the probabilistic jump search of simulated annealing with the convex polyhedron-based geometry search of Nelder-Mead Simplex method.…”

Section: Introductionmentioning

confidence: 99%

Optimal targeting of nonlinear chaotic systems using a novel evolutionary computing strategy

Wang¹,

Lyu

et al. 2016

Knowledge-Based Systems

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Control of chaotic systems to given targets is a subject of substantial and well-developed research issue in nonlinear science, which can be formulated as a class of multi-modal constrained numerical optimization problem with multi-dimensional decision variables. This investigation elucidates the feasibility of applying a novel population-based metaheuristics labelled here as Teaching-learning-based optimization to direct the orbits of discrete chaotic dynamical systems towards the desired target region. Several consecutive control steps of small bounded perturbations are made in the Teaching-learning-based optimization strategy to direct the chaotic series towards the optimal neighborhood of the desired target rapidly, where a conventional controller is effective for chaos control. Working with the dynamics of the well-known Hénon as well as Ushio discrete chaotic systems, we assess the effectiveness and efficiency of the Teaching-learning-based optimization based optimal control technique, meanwhile the impacts of the core parameters on performances are also discussed.Furthermore, possible engineering applications of directing chaotic orbits are discussed. Keywords:Chaos control; chaotic dynamics; optimization; computational intelligence;Teaching-learning-based optimization Highlights► Control of chaotic systems is formulated as constrained optimization problem.► Teaching-learning-based optimization is to direct the chaotic series.► The efficacy of TLBO based optimal control technique have been demonstrated.

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Directing orbits of chaotic systems using a hybrid optimization strategy

Cited by 19 publications

References 4 publications

Using Bat Algorithm with Levy Walk to Solve Directing Orbits of Chaotic Systems

Using Bat Algorithm with Levy Walk to Solve Directing Orbits of Chaotic Systems

Directing orbits of chaotic systems by particle swarm optimization

Optimal targeting of nonlinear chaotic systems using a novel evolutionary computing strategy

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