Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS

Wu, Jie; Xu, Wei; Wang, Xiaofeng; Ma, Ru-ru

doi:10.1016/j.chaos.2021.111582

Cited by 13 publications

(6 citation statements)

References 34 publications

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“…Comparations of the traditional finite-time, fixed-time, predefined-time, and the proposed smooth predefined-time control schemes. the traditional finite-time control [14][15][16][17][18][19][20][21][22], [32][33][34], [40] the traditional fixed-time control [23][24][25][26][27], [35,36,41] the traditional predefined-time control [29][30][31], [37,38,42] the proposed predefined-time smooth controllers (4), (12)…”

Section: Data Availability Statementmentioning

confidence: 99%

“…Fortunately, this deficiency has been overcome by leveraging the method of fixedtime stability analysis [23,24]. The topic of fixed-time chaotic stability with disturbances has been discussed via implementing the adaptive and SMC protocols [25,26]. For two different systems in noisy environment, the fixed-time chaotic synchronization can also be realized by smooth control [27].…”

Section: Introductionmentioning

confidence: 99%

“…Although the fixed-time stability is better than the traditional finite-time stable under certain circumstances [25][26][27], it is very hard to obtain an explicit upper-bound TE, which is related with the system parameters and may result in the overestimation for the convergence time. Fortunately, this issue can be solved via leveraging the method of predefined-time stability [28], so that the TE of convergence is not conservative comparing with the traditional finite-/fixed-time stable, which in fact is a real minimum.…”

Section: Introductionmentioning

confidence: 99%

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Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Ma,

Huang,

2023

Phys. Scr.

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This article investigates the predefined-time stabilization of nonlinear chaotic systems with applications in the permanent magnet synchronous motor (PMSM) system and Hindmarsh-Rose neuron model. Distinguished from the traditional predefined-time control methods, this investigation develops the smooth control protocols, in which the discontinuous absolute value and signum functions are not used anymore, so that the unfavorable chattering phenomenon can be avoided effectively. By the Lyapunov stability analysis, the sufficient condition is derived to achieve the predefined-time stable for nonlinear chaotic systems, in which the upper-bound time estimation (TE) of arriving at the stable state is explicit in contrast to the traditional finite-/fixed-time convergence. Specifically, the analytical results are successfully applied into stabilizing the PMSM system and Hindmarsh-Rose neuron model within the predefined-time. Finally, the numerical simulations for stabilizing the chaotic PMSM system and Hindmarsh-Rose neuron model verify the effectiveness and advantages of theoretical analysis.

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Section: Data Availability Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Ma,

Huang,

2023

Phys. Scr.

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“…Although the FxS and control of chaotic systems have been successfully applied into many fields, such as power systems [15], PMSMs [18], memristor chaotic circuits [29], FWS [30], and so forth, there are few results for the chaotic finance systems. Zhao et al…”

Section: Introductionmentioning

confidence: 99%

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

et al. 2022

Nonlinear Dyn

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This paper concerns the problem of fixed-time synchronization(FxS) of masterslave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand.Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

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“…About seventy years ago, Edward N. Lorenz observed the chaotic phenomenon, namely butterfly effect, in his old computer by simulating a three dimensional ordinary differential system [1]. After that, researchers from a variety of fields have developed many nonlinear chaotic models, for instance, the food web system [2], finance system [3], brushless DC motors system [4], permanent magnet synchronous motor(PMSM) system [5,6]. As we all known that the time evolution trajectories of nonlinear chaotic systems are completely distinct with respect to different initial states.…”

Section: Introductionmentioning

confidence: 99%

Realizing stochastic fixed-time synchronization between two nonlinear chaotic finance systems

Pan

et al. 2022

Preprint

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The issue of stochastic fixed-time synchronization(SFxS) between two nonlinear chaotic finance systems(CFSs) in noisy environment is addressed by this investigation. Two novel strategies, including the adaptive and fixed-time control, are integrated organically, which steers the CFSs to realize synchronization within a fixed-time, and meanwhile the controlling gains can be updated by the designed adaptive law. Particularly, the designed adaptive fixed-time controlling(AFC) scheme is differentiable, so that the chattering phenomenon can be alleviated and even eliminated effectively. Furthermore, by the stochastic Lyapunov stability, the sufficient criterion is derived for realizing the SFxS of CFSs, and the upper-bound expectation of settling-time(UET) is estimated as well. At last, the numerical experiments are arranged to verify the correctness and feasibility of analytical results, and the influence of noisy perturbation on the convergence rate is uncovered.

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Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS

Cited by 13 publications

References 34 publications

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

Realizing stochastic fixed-time synchronization between two nonlinear chaotic finance systems

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