Finite-time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Mobayen, Saleh

doi:10.1002/cplx.21624

Cited by 55 publications

(36 citation statements)

References 41 publications

(47 reference statements)

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“…The stabilization and tracking control of nonlinear and time-varying systems have important applications in electronics, mechanics and robotic systems [2][3][4][5][6]. Conventional feedback control methods do not obtain robustness and high performance when facing with the nonlinearities, uncertainties and external disturbances [7][8][9][10].…”

Section: Background and Motivationsmentioning

confidence: 99%

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Mobayen

2015

Nonlinear Dyn

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In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

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“…Nevertheless, during the reaching phase of SMC, the system can be destabilized by matched uncertainties and disturbances [9]. In SMC, the control signal is changed from one value to an infinite value with fast rate, and the mentioned action is undesirable in the practical dynamical systems [10,11]. This undesired switching effect is called chattering phenomenon [12].…”

Section: Introductionmentioning

confidence: 96%

Stability analysis and controller design for the performance improvement of disturbed nonlinear systems using adaptive global sliding mode control approach

Mobayen

Băleanu

2015

Nonlinear Dyn

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This paper addresses a novel adaptive global nonlinear sliding surface for a class of disturbed nonlinear dynamical systems. A nonlinear gain function is used in the sliding surface to change the damping ratio and improve the transient performance of the controlled system. Initially, to get a quick response, a low value of damping ratio is obtained using a constant gain matrix. As the response of the system approaches to the origin, the damping ratio of the controlled system is improved and the overshoot and settling time of the closed-loop system are reduced. A novel control law without chattering is designed to satisfy the elimination of the reaching phase and achieve the presence of the sliding around the surface right from the beginning. Moreover, the adaptive tuning control law eliminates the necessity of the knowledge about the bounds of the external disturbances. Illustrative simulations on Genesio chaotic system with different values of the initial conditions and external disturbances are presented to show the robustness and success of the suggested design.

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“…Recently, in [1,23,24,32,33,35], the parametric conditions for existence and direction of Neimark-Sacker bifurcation are investigated, and in [1,32,33,35] feedback chaos control strategies are implemented for controlling chaos and bifurcations in host-parasitoid models. Moreover, for state-feedback control design based on the matrix inequality approaches, we refer to [63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Din¹,

Hussain²

2018

Asian Journal of Control

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In this paper, a new density-dependent host-parasitoid model is proposed. The modification is based on density-dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium point are also investigated. It is demonstrated that system endures Neimark-Sacker bifurcation for wide range of bifurcation parameter. In order to control chaos due to emergence of Neimark-Sacker bifurcation, two feedback control strategies, that is, OGY and hybrid control methods are implemented. Finally, all mathematical analysis, particularly, Neimark-Sacker bifurcation, chaos control strategies, and global asymptotic stability of unique positive point are verified with the help of numerical simulations.

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“…Finite-time control techniques have been proposed for synchronization of some pratical chaotic systems by Sun, Wu, Bai, Wei, and Sun (2016) ;Liu, Li, and Feng (2016) and Du, Li, and Qian (2011). Moreover, Mobayen (2016) studied finite-time synchronization of chaotic systems with matched and unmatched uncertainties via LMI technique. A control Lyapunov function (CLF) scheme has also been reported for finite-time synchronization of chaotic systems (Wang, Han, Xie, & Zhang, 2009;Yu, 2010).…”

Section: Introductionmentioning

confidence: 99%

Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros

Mohammadpour

Binazadeh

2018

Systems Science & Control Engineering

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This paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finitetime stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing-Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller. ARTICLE HISTORY

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“…In [27], the SMC surface design is concerned with multi-objective mixed H 2 /H ∞ optimization for the perturbed nonlinear systems in the existence of matched and unmatched uncertainties and disturbances. In [14], the asymptotic boundedness of the state errors using SMC technique for a class of chaotic systems with matched and unmatched uncertainties is proved. In [16], a terminal sliding mode design approach using composite nonlinear feedback technique is provided to guarantee the finite-time boundedness of the state errors during the sliding mode.…”

Section: Introductionmentioning

confidence: 99%

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Mobayen¹,

Tchier²

2016

Kybernetika

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A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems Kybernetika, Vol. 51 (2015) This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme.,

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Finite-time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Cited by 55 publications

References 41 publications

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Stability analysis and controller design for the performance improvement of disturbed nonlinear systems using adaptive global sliding mode control approach

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

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