A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints

Jafari, Sajad; Sprott, Julien Clinton; Pham, Viet–Thanh; Golpayegani, Seyed Mohammad Reza Hashemi; Jafari‬, Amir Homayoun

doi:10.1142/s021812741450134x

Cited by 71 publications

(31 citation statements)

References 77 publications

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“…The error norm can be extended to be a cost function having the lowest cost when the trajectory between systems is close to each other [28][29][30]. The cost function in this work is defined by the formula below.…”

Section: Theoremmentioning

confidence: 99%

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

Cheng

Chao

2018

Applied Sciences

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This article addresses trajectory tracking between two non-identical systems with chaotic properties. To study trajectory tracking, we used the Rossler chaotic and resistive-capacitive-inductance shunted Josephson junction (RCLs-JJ) model in a similar phase space. In order to achieve goal tracking, two stages were required to approximate target tracking. The first stage utilizes the active control technique to transfer the output signal from the RCLs-JJ system into a quasi-Rossler system. Next, the RCLs-JJ system employs the proposed iterative learning control scheme in which the control signals are from the drive system to trace the trajectory of the Rossler system. The numerical results demonstrate the validity of the proposed method and the tracking system is asymptotically stable.

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Section: Theoremmentioning

confidence: 99%

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

Cheng

Chao

2018

Applied Sciences

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“…As investigated by many researchers [8][9][10][11][12][13][14][15], chaotic attractors with no equilibrium are hidden thus making NCS 2 and NCS 4 hidden attractors.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…Control of such hidden oscillations is a big challenge because of the multistability nature of the systems [6,7]. Chaotic attractors are with no equilibrium points [8][9][10][11][12][13][14][15], with only stable equilibria [16][17][18][19], and with curves of equilibria [20]. Fractional order with no equilibrium systems with its FPGA implementation has also been reported recently [21,22].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaotic Chameleon: Fractional Order FPGA Implementation

2017

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There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA) implementations of the systems with their power and resource utilization are presented.

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“…Here, we propose using the geometrical similarity between these attractors as the objective function for parameter estimation [18,19].…”

Section: The Optimization Problemmentioning

confidence: 99%

Using Modified Intelligent Experimental Design in Parameter Estimation of Chaotic Systems

2017

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Computational modeling plays an important role in prediction and optimization of real systems and processes. Models usually have some parameters which should be set up to the proper value. Therefore, parameter estimation is known as an important part of the modeling and system identification. It usually refers to the process of using sampled data to estimate the optimum values of parameters. The accuracy of model can be increased by adjusting its parameters to the optimum value which need a richer dataset. One simple solution for having a richer dataset is increasing the amount of data, but that can be costly and time consuming. When using data from animals or people, it is especially important to have a proper plan. There are several available methods for parameter estimation in dynamical systems; however there are some basic differences in chaotic systems due to their sensitivity to initial condition (butterfly effect). Accordingly, in this paper, a new cost function which is proper for chaotic systems is applied to the chaotic one-dimensional map. Then the efficiency of a newly introduced intelligent method experimental design in extracting proper data is investigated. The results show the success of the proposed method.

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A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints

Cited by 71 publications

References 77 publications

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

Hyperchaotic Chameleon: Fractional Order FPGA Implementation

Using Modified Intelligent Experimental Design in Parameter Estimation of Chaotic Systems

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