Robust observer-based stabilizer for perturbed nonlinear complex financial systems with market confidence and ethics risks by finite-time integral sliding mode control

Mirzaei, Mojtaba; Mirzaei, Mohaddeseh; Aslmostafa, Ehsan; Asadollahi, Mostafa

doi:10.1007/s11071-021-06695-7

Cited by 10 publications

(10 citation statements)

References 45 publications

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“…have deployed the fixed-time integral SMC technique to stabilize the CFS [35]. Recently, Ma et al have designed the adaptive fixed-time control(AFC) scheme to synchronize drive-response CFSs [36].…”

Section: Introductionmentioning

confidence: 99%

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

Wu,

Pan,

et al. 2023

Int. J. Mod. Phys. C

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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 analysis, 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, the influence of noisy perturbation on the convergence rate is uncovered, and the interesting similar Dragon–King events are observed.

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Section: Introductionmentioning

confidence: 99%

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

Wu,

Pan,

et al. 2023

Int. J. Mod. Phys. C

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“…Thus, the accomplished convergence time in these methods is infinite, which results in an undesirable attitude in practice. Accordingly, finite-time synchronization methods have been proposed to address the encountered problem and in recent years the mentioned approach has been investigated to the large extent (Aslmostafa et al, 2021b; Chen et al, 2018; Mirzaei et al, 2021c; Ning et al, 2020; Xi et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

Mirzaei

Aslmostafa

Asadollahi

et al. 2022

Journal of Vibration and Control

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In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations.

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“…Stabilization is an essential control problem. There are abundant results related to the stabilization of various dynamical models like linear systems (Brockett and Liberzon, 2000), non-linear systems (Mirzaei et al, 2021), and networked systems (Liu et al, 2021). Meanwhile, different control methods, such as output feedback (Jia et al, 2020) and event-triggered strategies (Peng and Ai, 2019), have also been proposed to implement the stabilization of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

The feedback stabilization of finite-state fuzzy cognitive maps

Xiaojie

Luo

2022

Transactions of the Institute of Measurement and Control

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Fuzzy cognitive maps (FCMs) are a kind of cognitive model for knowledge representation and causal inference. Meanwhile, as fuzzy dynamical systems, FCMs have also been widely applied in the control-related fields, such as mobile robots, unmanned aerial vehicles (UAVs), and industrial controls. However, the existing works mainly focused on the practical applications but lacked the necessary theoretical discussions related to the FCM-based control mechanism. As is known, stabilization is one of the fundamental issues in the control fields. Till date, rigorous research on the stabilization of FCMs is still an issue to be studied. In this article, using state feedback control method, the global stabilizations of finite-state FCMs are investigated. First, utilizing the semi-tensor product (STP) of matrices, the algebraic expression of FCM can be derived. Some theorems ensure the sufficient condition for the existence of the state feedback controller of the global stabilization. Second, the constructive design processes of state feedback controllers are discussed in detail. Third, the global stabilization is further extended into partial stabilization, where only specific concepts of FCMs can be stabilized. The corresponding theoretical analysis is implemented. Finally, the effectiveness of the proposed methods is verified by several examples.

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Robust observer-based stabilizer for perturbed nonlinear complex financial systems with market confidence and ethics risks by finite-time integral sliding mode control

Cited by 10 publications

References 45 publications

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

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

Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

The feedback stabilization of finite-state fuzzy cognitive maps

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