An exponential polynomial observer for synchronization of chaotic systems

Mata-Machuca, Juan L.; Martínez-Guerra, Rafael; Aguilar-López, Ricardo

doi:10.1016/j.cnsns.2010.01.040

Cited by 20 publications

(11 citation statements)

References 28 publications

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“…Looking to avoid time derivatives of the output consider γ 2 =η 2 − K 2,0 a y 1 as an auxiliary variable, now we take (34) and after some algebraic manipulations we have γ (α) 2 = K 2,0 y 1 − γ 2 + K 2,0 a y 1 + K 2,1 a y 1 + K 2,1 D (−α) y 1 − γ 2 + K 2,0 a y 1 + K 2,0 y 1 + K 2,2 a D (−α) y 1 + K 2,2 D (−2α) y 1 − γ 2 + K 2,0 a y 1…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

Cruz-Victoria

Martínez-Guerra

Pérez-Pinacho

et al. 2015

Applied Mathematics and Computation

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Section: Numerical Resultsmentioning

confidence: 99%

“…A variety of observer-based approaches have been proposed for the synchronization of chaotic systems, which include the exponential polynomial observer [2], sliding observer [3], higher order sliding observer [4], fuzzy disturbance observer [5], etc.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

Cruz-Victoria

Martínez-Guerra

Pérez-Pinacho

et al. 2015

Applied Mathematics and Computation

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“…In [16] a polynomial observer, a reduced order observer and a sliding mode observer are used in order to estimate and reconstruct the system states and faults for the case of multiple available outputs. In [17], the polynomial observer is used for the synchronization of chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Fault Estimation for a Quad-Rotor MAV Using a Polynomial Observer

Aguilar-Sierra¹,

Flores²,

Salazar³

et al. 2013

J Intell Robot Syst

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International audienceThis work addresses the problem of fault detection and diagnosis (FDD) for a quad-rotor mini air vehicle (MAV). Actuator faults are considered on this paper. The basic idea behind the proposed method is to estimate the faults signals using the extended state observers theory. To estimate the faults, a polynomial observer (Aguilar et al. 2011; Mata-Machuca et al., Commun Nonlinear Sci Numer Simul 15(12):4114-4130, 2010, BioSystems 100(1):65-69, 2010) is presented by using the available measurements and know inputs of the system. In order to investigate the diagnosability properties of the system, a differential algebra approach is proposed (Cruz-Victoria et al., J Frankl Inst 345(2):102-118, 2008; and Martinez-Guerra and Diop, IEE P-Contr Theor Ap 151(1):130-135, 2004). The effectiveness of the methodology is illustrated by means of numerical simulations

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“…A variety of observer-based approaches have been proposed for the synchronization of chaotic systems, which include the exponential polynomial observer [16], sliding observer [17], adaptive sliding observer [18], higher order sliding mode observer [19], fuzzy disturbance observer [20], Thau observer [21]. Synchronization of fractional-order chaotic systems was studied by Deng and Li [22] who carried out synchronization in case of the fractional Lu system.…”

Section: Introductionmentioning

confidence: 99%

“…Among the array of methods proposed for synchronization of chaotic dynamics, observer based methods [16][17][18][19][20][21] are the focal point of interest in the field of integer chaos synchronization, but a lack of observer schemes impedes designing and stability analysis under in fractional systems. This is why we developed a sliding observer scheme for synchronizing fractional-order chaotic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Delavari¹,

Senejohnny²,

Băleanu³

2012

Open Physics

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Abstract:In this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.PACS (2008)

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An exponential polynomial observer for synchronization of chaotic systems

Cited by 20 publications

References 28 publications

Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

Fault Estimation for a Quad-Rotor MAV Using a Polynomial Observer

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

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