Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Luo, Runzi; Huang, Meng; Su, Haipeng

doi:10.1155/2019/8417536

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…Its chaotic behavior is shown in Figures 6-8. The state trajectories of the system (21). To stabilize the Matouk system, the internal uncertainties are:…”

Section: Figurementioning

confidence: 99%

“…In the same year, [20] introduced an adaptive sliding mode disturbance observer-based finite time control approach for uncertain nonlinear systems. In addition, [21] established various criteria for the resilient management and synchronization of a class of 3D fractional-order chaotic systems with external disturbances in 2019. A class of ambiguous single-input, singleoutput nonlinear systems with unclear control direction and disturbances was taken into consideration in [22].…”

Section: Introductionmentioning

confidence: 99%

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Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

et al. 2023

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This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

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“…Its chaotic behavior is shown in Figures 6-8. The state trajectories of the system (21). To stabilize the Matouk system, the internal uncertainties are:…”

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

et al. 2023

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“…10 In 2019, another interesting research topic would be synchronizing a three-dimensional fractional-order system with external disturbances. 11 This article described the synchronization of a class of fractional-order systems with external disturbances. The global stability of the synchronizing manifold is studied by including a power integrator control system that generalized the standard back-stepping approach.…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞output feedback control of uncertain fractional-order systems subject to input saturation

Fiuzy

Shamaghdari

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

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“…Combining adaptive control and sliding mode method, a robust sliding mode controller was designed in Reference 12 to realize the synchronization of two fractional order chaotic Genesio-Tesi systems with parameter uncertainties. Article 13 resolved the control and synchronization problem of 3D uncertain fractional-order chaotic systems by taking advantage of the adding one power integrator approach.…”

Section: Introductionmentioning

confidence: 99%

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

Luo

et al. 2021

Adaptive Control & Signal

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This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.

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Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Cited by 7 publications

References 20 publications

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Robust H_∞output feedback control of uncertain fractional-order systems subject to input saturation

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

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Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Cited by 7 publications

References 20 publications

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Robust H∞output feedback control of uncertain fractional-order systems subject to input saturation

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

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Product

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Robust H_∞output feedback control of uncertain fractional-order systems subject to input saturation