Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control

Su, Haipeng; Luo, Runzi; Fu, Jiaojiao; Huang, Meng

doi:10.1016/j.isatra.2021.02.012

Cited by 14 publications

(8 citation statements)

References 31 publications

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“…In the following simulation, we select ò = 7/9 and keep the values of other parameters as well as initial values unchanged. All variables x i , i = 1, 2, 3, in the chaotic PMSM system (10) will also converge to the stable state within T c , illustrated in figure 10(a), by using the traditional control scheme (26), and the time evolutions of controllers u i , i = 1, 2, 3, are displayed in figure 10(b), where there exists chattering phenomena obviously when the controllers approach to zero. The controlling signals switch frequently around zero.…”

Section: Comparative Analysismentioning

confidence: 99%

“…Fortunately, this deficiency has been overcome by leveraging the method of fixedtime stability analysis [23,24]. The topic of fixed-time chaotic stability with disturbances has been discussed via implementing the adaptive and SMC protocols [25,26]. For two different systems in noisy environment, the fixed-time chaotic synchronization can also be realized by smooth control [27].…”

Section: Introductionmentioning

confidence: 99%

“…Although the fixed-time stability is better than the traditional finite-time stable under certain circumstances [25][26][27], it is very hard to obtain an explicit upper-bound TE, which is related with the system parameters and may result in the overestimation for the convergence time. Fortunately, this issue can be solved via leveraging the method of predefined-time stability [28], so that the TE of convergence is not conservative comparing with the traditional finite-/fixed-time stable, which in fact is a real minimum.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Ma,

Huang,

2023

Phys. Scr.

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This article investigates the predefined-time stabilization of nonlinear chaotic systems with applications in the permanent magnet synchronous motor (PMSM) system and Hindmarsh-Rose neuron model. Distinguished from the traditional predefined-time control methods, this investigation develops the smooth control protocols, in which the discontinuous absolute value and signum functions are not used anymore, so that the unfavorable chattering phenomenon can be avoided effectively. By the Lyapunov stability analysis, the sufficient condition is derived to achieve the predefined-time stable for nonlinear chaotic systems, in which the upper-bound time estimation (TE) of arriving at the stable state is explicit in contrast to the traditional finite-/fixed-time convergence. Specifically, the analytical results are successfully applied into stabilizing the PMSM system and Hindmarsh-Rose neuron model within the predefined-time. Finally, the numerical simulations for stabilizing the chaotic PMSM system and Hindmarsh-Rose neuron model verify the effectiveness and advantages of theoretical analysis.

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Section: Comparative Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Ma,

Huang,

2023

Phys. Scr.

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“…In Chen et al (2019), the fixed-time stability of system was realized, yet the unknown disturbance was not considered. In Su et al (2021), for the system subject to bounded disturbance with a known upper boundary, a sliding mode theory–based FTC tactic was presented. In Chen et al (2022), a fixed-time H ∞ control (FT H ∞ C ) scheme was presented for the system in the presence of bounded disturbance, where the disturbance was restricted by an unknown upper boundary.…”

Section: Introductionmentioning

confidence: 99%

Disturbance observer-based fixed-time control for nonlinear systems with multiple disturbances

Gao

Wei

et al. 2023

Transactions of the Institute of Measurement and Control

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The fixed-time control is researched for the nonlinear system subject to multiple disturbances, which contain an external disturbance with unknown frequency and an unknown bounded disturbance. An adaptive nonlinear disturbance observer is devised to estimate the unknown frequency disturbance generated by an exogenous system. On this foundation, a composite fixed-time control scheme is proposed by combining the [Formula: see text] control and the fixed-time theory. It guarantees that the expected control performances of system can be achieved under the existence of multiple disturbances. Eventually, the validity of the control scheme is proved via simulation examples.

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“…In Wang et al (2020b), the problem of fixed-time chaos suppression and stabilization of a class of Lorenz systems with uncertain parameters has been investigated. In Su et al (2021), the fixed-time control problem of perturbed chaotic systems by virtue of SMC has been addressed. In the latter two works, specialized types of systems have been examined, and for the purpose of including a wide range of systems, a generalized class of systems must be taken into consideration.…”

Section: Introductionmentioning

confidence: 99%

Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

Mirzaei

Aslmostafa

Asadollahi

et al. 2022

Journal of Vibration and Control

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In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations.

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Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control

Cited by 14 publications

References 31 publications

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

Disturbance observer-based fixed-time control for nonlinear systems with multiple disturbances

Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

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