Optimal control of nonlinear systems to given orbits

Korzinov, L.; Mees, A. I.; Starobinets, I. M.

doi:10.1016/s0167-6911(97)00048-0

Cited by 20 publications

(3 citation statements)

References 12 publications

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“…In recently years, growing interests from physics, chemistry, biology, electronics, controls and instrumentation have stimulated the studies of chaos so as to improve the industrial and manufacturing systems and processes which exhibit chaotic phenomena [1]. Control of chaotic systems is one of important and well-developed research issues in nonlinear science [2][3][4], and it is possible that a minute perturbation of the control parameter could redirect chaos towards the desired region and stabilize it [5]. In the last decade, chaotic control has been shown to cover a wide spectrum of real world applications in engineering [6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…Paskota et al [22] applied the optimal control theory to calculate an open-loop controller and direct the orbit of a chaotic system towards the neighborhood of the desired target. Abarbanel et al [3] demonstrated the use of an explicit single-step control method for directing a nonlinear system to the target orbit and maintaining it there.…”

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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“…(synchronization) 17 [1] (controlled synchronization) ( ) ( ) 20 90 [2][3][4][5][6][7][8][9] [10] [11,12] [13] [14][15][16] (continuous-time design, CTD) [17,18] (1)…”

Section: (Introduction)mentioning

confidence: 99%

Synchronization of nonlinear systems with stair-step signal

Huang

Kang

Yin

2008

2008 27th Chinese Control Conference

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From the viewpoint of computer control, the synchronization of nonlinear systems is investigated. The controlled synchronization problem with stair-step signal is presented. The synchronization error controlled by the stair-step signal is analyzed and it is proved with Lyapunov method that if the Euclid norm of the control signal is no more than the norm of the synchronization error times a constant, and the signal makes the Euler approximate model of the error exponentially stable, then the stair-step signal will make the slave synchronized with the master.

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Chaos control using least-squares support vector machines

Suykens

Vandewalle

1999

Int. J. Circ. Theor. Appl.

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Optimal control of nonlinear systems to given orbits

Cited by 20 publications

References 12 publications

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

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

Synchronization of nonlinear systems with stair-step signal

Chaos control using least-squares support vector machines

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