Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

Chen, Yuquan; Wang, Bing; Chen, YangQuan; Wang, Yong

doi:10.3390/fractalfract6110678

Cited by 7 publications

(3 citation statements)

References 39 publications

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“…The findings of the research were reported in [32], and one of the main takeaways was the development of a new synchronized fixed-time TSM technique for use with fractional chaotic systems. The authors in [33] suggested a non-singular fixed-time sliding mode method as a solution to the non-linear chaotic system. In order to better accommodate scattered quadrotors, an improved adaptive fractional-order rapid integral TSMC was devised [34].…”

Section: Related Workmentioning

confidence: 99%

Trajectory Tracking Control of Euler–Lagrange Systems Using a Fractional Fixed-Time Method

et al. 2023

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The results of this research provide fixed-time fractional-order control for Euler–Lagrange systems that are subject to external disturbances. The first step in the process of developing a new system involves the introduction of a method known as fractional-order fixed-time non-singular terminal sliding mode control (FoFtNTSM). The advantages of fractional-order calculus and NTSM are brought together in this system, which result in rapid convergence, fixed-time stability, and smooth control inputs. Lyapunov analysis reveals whether the closed-loop system is stable over the duration of the time period specified. The performance of the suggested method when applied to the dynamics of the Euler–Lagrange system is evaluated and demonstrated with the help of computer simulations.

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Section: Related Workmentioning

confidence: 99%

Trajectory Tracking Control of Euler–Lagrange Systems Using a Fractional Fixed-Time Method

et al. 2023

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“…Furthermore, fractional-order (Fo) control has been incorporated with SMC to improve the performance of the controller [21][22][23]. Fractional-order control, which has been in use for the last three centuries and is concerned with derivatives and integrals of a non-integer order, was recently rediscovered by scientists and engineers and is being put to use in a variety of different fields [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Control Design for Euler–Lagrange Systems Using Fixed-Time Fractional Integral Sliding Mode Scheme

Ahmed,

Azar,

Tounsi

et al. 2023

Fractal Fract

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This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method.

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“…Fractional-order differential equations, which are actually generalizations of integer order calculus, deal with derivatives and integrals with non-integer orders. These equations have a unique feature which is the description of the memory effect [6][7][8]. Fractional derivative chaotic systems are now an important topic of study in nonlinear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

Liu

Muhsen²,

Shateyi

et al. 2023

Fractal Fract

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In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag–Leffler attractive sets (MLASs) and Mittag–Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results.

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Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

Cited by 7 publications

References 39 publications

Trajectory Tracking Control of Euler–Lagrange Systems Using a Fractional Fixed-Time Method

Trajectory Tracking Control of Euler–Lagrange Systems Using a Fractional Fixed-Time Method

Adaptive Control Design for Euler–Lagrange Systems Using Fixed-Time Fractional Integral Sliding Mode Scheme

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

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