Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Hajipour, Ahmad; Tavakoli, Hamidreza

doi:10.1142/s021812741750198x

Cited by 20 publications

(10 citation statements)

References 30 publications

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“…The following financial system has been investigated in many existing literature( [1][2][3][4][5][6][7][8][9]),…”

Section: System Descriptionmentioning

confidence: 99%

Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Rao¹

2020

Preprint

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Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global financial crisis often erupts periodically, which illuminates that the global stability in the classical sense is actually meaningless. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.

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“…The following financial system has been investigated in many existing literature( [1][2][3][4][5][6][7][8][9]),…”

Section: System Descriptionmentioning

confidence: 99%

Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Rao¹

2020

Preprint

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“…wheref = −(D + 2ˆ )q −K q is an estimate of f . And the proposed modified adaptive controller is designed asû =û eq + u sw (23) whereû eq is shown in (22) and u sw remains the same as (18).…”

Section: B Design Of Adaptive Fractional Order Dynamic Sliding Mode Controlmentioning

confidence: 99%

“…Fei and Lu [21] proposed an adaptive fractional order sliding mode control method for a Z-axis gyroscope where a neural network is used to alleviate chattering. In [22], Ahmad and Hamidreza analyzed dynamics of chaotic fractional order systems under adaptive sliding mode control method. In [23], Ali and Hamed proposed a new fractional order dynamic sliding mode method for a class of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Control of Z-Axis MEMS Gyroscope Using Adaptive Fractional Order Dynamic Sliding Mode Approach

et al. 2019

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This paper proposes a states feedback control method for Z-axis MEMS gyroscopes using fractional calculus and adaptive dynamic sliding mode control method. A new sliding mode control method is proposed to achieve trajectory tracking by adding a fractional order term in the conventional sliding manifold. The new proposed sliding surface contains integer order terms as well as fractional order terms and thus can provide an extra degree of freedom. Besides, in the presence of unknown system parameters, some adaptive laws containing the new designed sliding manifold are proposed to online tune controller parameters. All adaptive laws are derived in the stability framework and the stability of the control system is also guaranteed according to the Lyapunov stability theory and. Simulations results on a Z-axis vibrating gyroscope are provided to illustrate the effectiveness of the control method.INDEX TERMS Adaptive control, dynamic sliding mode control, gyroscope, fractional order calculus.

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“…In the literature, several methods have been proposed to achieve this goal. We have among others, the linear feedback control [7], adaptive control [8,9], sliding mode control [10], Lyapunov-based nonlinear control [11], adaptive sliding mode control [12], etc. Recently, for the stabilization of dynamical systems, different results have been obtained in the literature in fields as diverse as varied.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

Dousseh

Ainamon

Miwadinou

et al. 2021

Mathematical Problems in Engineering

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In this paper, adaptive control and adaptive synchronization of an integer and fractional order new financial system with unknown constant parameters are studied. Based on Lyapunov’s stability theory, an adaptive control law is designed to asymptotically stabilize the state variables of the system to the origin in integer and fractional order cases. By the same theory, an adaptive synchronization law is designed to perform the identical synchronization of the new financial system in the cases of integer and fractional order with unknown constant parameters. Numerical simulations are carried out in order to show the efficiency of the theoretical results.

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Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Cited by 20 publications

References 30 publications

Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Control of Z-Axis MEMS Gyroscope Using Adaptive Fractional Order Dynamic Sliding Mode Approach

Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

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