Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Wang, Xuhuan

doi:10.1186/s13662-018-1470-9

Cited by 10 publications

(10 citation statements)

References 42 publications

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“…5 In recent years, many important results had been achieved in the stability analysis and control research of fractional order nonlinear systems. For example, Wang 6 extended backstepping control scheme to fractional order system and studied problem of Mittage-Leffler stabilization of fractional order nonlinear system. Ding et al 7 proposed a fractional order backstepping controller for a class of fractional order nonlinear strict-feedback system with both unknown disturbance.…”

Section: Introductionmentioning

confidence: 99%

Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

Chen

Cao

Yuan

et al. 2021

Measurement and Control

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This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

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Section: Introductionmentioning

confidence: 99%

Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

Chen

Cao

Yuan

et al. 2021

Measurement and Control

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“…So it has that s(0) = 0 and C 0 D ε t = RL 0 D ε t . According to (31), the following relationship is established:…”

Section: Stability Analysis Of Fod-gftsmc Whenmentioning

confidence: 99%

Global Fast Terminal Sliding Mode Control Based on Fractional Order Differentiation for Angular Position Synchronization Control of PMSM

Shu

Jiang

et al. 2022

IEEJ Transactions Elec Engng

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This paper is aimed at improve accuracy of angular position synchronization control of Permanent Magnet Synchronous Motor driving system. Traditional PID controller could not meet requirement due to poor dynamic characteristics. The Global Fast Terminal Sliding Mode Control (GFTSMC) has good ant-disturbance ability, could make system more robust and realize synchronization control of angular position. But due to error in load torque observation, system state convergence error will be caused, which will reduce the accuracy of synchronization. In this paper, fractional-order differentiation is used to replace the nonlinear part of GFTSMC, constructed Fractional Order Differentiation-GFTSMC (FOD-GFTSMC) controller to improve accuracy of synchronization. Theoretical analysis will be used to demonstrate that this control strategy could improve convergence accuracy of system state, reduces error of synchronization, and some experiments will be carried out to verify that this kind of controller has high synchronization accuracy, fast dynamic response ability and strong robustness.

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“…The control-Lyapunov function is the best known method to analyse the nonlinear control systems (see Ibañez et al, 2005). However, designing a control-Lyapunov function for NFC systems is a complex work (Wang, 2018). Robust stability and stabilization of fractional-order interval systems with 0 < α < 1 order have been studied in Lu and Chen (2010).…”

Section: Introductionmentioning

confidence: 99%

On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

Yavari

Nazemi

2021

Transactions of the Institute of Measurement and Control

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In this paper, stabilization of the nonlinear fractional order systems with unknown control coefficients is considered where the dynamic control system depends on the Caputo fractional derivative. Related to the nonlinear fractional control (NFC) system, an infinite-horizon optimal control (OC) problem is first proposed. It is shown that the obtained OC problem can be an asymptotically stabilizing control for the NFC system. Using the help of an approximation, the Caputo derivative is replaced with the integer order derivative. The achieved infinite-horizon OC problem is then converted into an equivalent finite-horizon one. According to the Pontryagin minimum principle for OC problems and by constructing an error function, an unconstrained minimization problem is defined. In the optimization problem, trial solutions are used for state, costate and control functions where these trial solutions are constructed by using a two-layered perceptron neural network. A learning algorithm with convergence properties is also provided. Two numerical results are introduced to explain the main results.

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Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Cited by 10 publications

References 42 publications

Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

Global Fast Terminal Sliding Mode Control Based on Fractional Order Differentiation for Angular Position Synchronization Control of PMSM

On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

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