Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Song, Xiaona; Song, Shuai; Tejado, Inés; Liu, Leipo; Zhang, Lei

doi:10.1155/2017/9562818

Cited by 12 publications

(11 citation statements)

References 35 publications

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“…in which, K D , K P , K I , µ 1 and µ 2 are positive real constants and b ∈ (0, 1) is a positive number. Similar to (16), the condition σ(t) is satisfied for (24), consequently,…”

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

“…Theorem 4. Consider PID sliding surface (24) and relations (25) and (26). Then, the nonlinear PID sliding surface system ( 27) is finite-time stable, and zero is the asymptotic equilibrium point for (24).…”

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

“…For dealing with nonlinear FO systems, ref. [24] suggests a synchronization utilizing a non-singular T-S-fuzzy SMC methodology. The authors of [25] delve into a class of complex non-identical-order chaotic FO systems, proposing an adaptive SMC method tailored to such scenarios.…”

mentioning

confidence: 99%

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A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Roohi,

Mirzajani,

Basse-O’Connor

2023

Mathematics

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Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of different system classes. This paper introduces a novel single-input finite-time PID sliding mode control (SMC) technique to stabilize a specific group of unknown 4-dimensional chaotic fractional-order (FO) laser systems. By combining the PID concept with the FO-version of the Lyapunov stability theory, a novel finite-time PID SMC strategy has been developed, which effectively mitigates chaotic behavior in the mentioned unknown 4-dimensional chaotic FO laser system. This method makes use of a characteristic of FO chaotic systems known as boundedness, which is used here. Notably, the control input’s sign function, which is responsible for undesirable chattering, is transformed into the fractional derivative of the control input. This transformation results in a smooth and chattering-free control input, further enhancing the method’s performance. To demonstrate the efficacy of the proposed chattering-free–finite-time PID SMC technique, two numerical scenarios are presented, showcasing its efficient performance in stabilizing the unknown 4-dimensional chaotic FO laser system. These scenarios serve as illustrations of the method’s potential for practical applications.

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“…in which, K D , K P , K I , µ 1 and µ 2 are positive real constants and b ∈ (0, 1) is a positive number. Similar to (16), the condition σ(t) is satisfied for (24), consequently,…”

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

Section: Design Of the Finite-time Pid Smcmentioning

confidence: 99%

See 1 more Smart Citation

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Roohi,

Mirzajani,

Basse-O’Connor

2023

Mathematics

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“…It has also been studied in the control and synchronization of time-invariant/varying and SMC chaotic systems [23,24]. In addition, studies have been made on determining the surface of fractional chaotic systems with fuzzy logic [25,26]. In the study, rather than determining the surface, the chattering amplitude was determined by fuzzy logic and synchronization was achieved with the control rule.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control

Ramakrishnan

Çimen

Akgül

et al. 2022

Mathematical Problems in Engineering

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A linear resistive capacitive inductive shunted model of a Josephson junction with a topologically nontrivial behaviour is considered in this paper. We have considered a fractional-order flux-controlled memristor to effectively model the feedback flux effects across the Josephson junction (JJ). The mathematical model of the proposed JJ oscillator is derived, and the dimensionless model is used to study the various dynamical properties of the oscillator. The stability plot shows that the proposed oscillator has both stable and unstable regions of oscillations for different choices of equilibrium points and fractional order. The bifurcation plots are presented to understand the route to crisis, and we have also shown that the oscillator has regions of coexisting attractors. We have also achieved the synchronization of the proposed oscillator using fuzzy sliding mode control with the master and slave systems considered with different parameter sets. The chattering amplitude is estimated by using the fuzzy logic, and it is used in the synchronization algorithm to minimize the error.

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“…Additionally, the response time of the system and achieving the desired value within a finite time have not been extensively investigated. In Song et al [53], a nonsingular terminal fuzzy SMC approach is suggested for a special category of chaotic systems that are fractional-order systems simultaneously. In Fei et al [51], other fractional-order terminal sliding mode control (FTSMC) technique is applied to synchronize chaotic systems with known upper bound of disturbances.…”

mentioning

confidence: 99%

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

Sepestanaki

Soofi

Barhaghtalab

et al. 2023

Math Methods in App Sciences

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This study proposes the adaptive continuous barrier function as the fractional‐order control system using the terminal sliding mode control technique with chattering‐free property to stabilize chaotic systems that have unknown uncertainties. The important reason for using the fractional‐order controller is its greater flexibility than the integer‐order controller. Using adaptive approach and Lyapunov's stability theory, an adaptive continuous barrier fractional‐order chattering‐free finite‐time controller for a category of chaotic systems with the unknown uncertainties and external disturbances is presented. The suggested controller can stabilize the chaotic system excellently with a continuous and smooth control law even without knowing the boundaries and in the presence of unknown disturbances due to the model uncertainties. According to MATLAB simulation results, the high efficiency of the suggested control technique to control the chaotic systems in the attendance of unknown perturbations is obviously confirmed.

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Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Cited by 12 publications

References 35 publications

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

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