An LMI approach to robust synchronization of a class of chaotic systems with gain variations

Asheghan, Mohammad Mostafa; Beheshti, Mohammad Taghi Hamidi

doi:10.1016/j.chaos.2009.03.152

Cited by 19 publications

(6 citation statements)

References 11 publications

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“…In Huang and Feng (2008), based on delayed feedback control, a robust H ∞ synchronization problem is presented for chaotic Lur’e systems with an energy bounded input noise. In Asheghan and Beheshti (2009), a robust chaos synchronization approach via linear state-feedback control law is presented for uncertain chaotic systems with perturbation in parameters, gain variations, and external disturbances. In Chen and Chen (2009a), a robust synchronization controller based on disturbance-observer is offered for chaotic systems with parametric uncertainties and unknown external disturbances.…”

Section: Introductionmentioning

confidence: 99%

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

Mobayen

Ren

et al. 2017

Journal of Vibration and Control

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This paper proposes an adaptive robust finite-time control method based on a global sliding surface for the synchronization of a class of chaotic systems. New chattering-free control laws are designed to guarantee the removal of the reaching mode and realize the existence of the sliding mode around the designed surface right from the first moment. The proposed adaptive-tuning controllers eliminate the requirement of knowledge about disturbance bounds. Using the suggested control technique, superior master–slave synchronization is achieved, the chattering problem is fully solved, and the amplitudes of the control signals are noticeably decreased. Demonstrative simulation results for a Lü chaotic system are presented to indicate the efficiency and usefulness of the proposed scheme. In the end, using a state-feedback controller, we obtain a four-dimensional system with two interesting features. First, some hyperchaotic solutions are proposed, and then a continuous bifurcation diagram showing chaos for a wide range of bifurcation parameter is presented.

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Section: Introductionmentioning

confidence: 99%

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

Mobayen

Ren

et al. 2017

Journal of Vibration and Control

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“…So, synchronization of chaotic systems with uncertainties and external disturbances is effectively significant in the applications. In this direction, a number of techniques have been proposed for synchronization of uncertain identical as well as nonidentical chaotic [9][10][11][12][13][14][15][16][17][18]. All above mentioned techniques are based on with fully (or partially) known parameters for the systems.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

Khan

Shahzad

2013

Complexity

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In this computational study, we synchronize the Circular Restricted Three Body Problem (CRTBP) with Lorenz Hyper Chaotic System (LHCS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the implemented technique for the two non‐identical systems under consideration are being done using Mathematica. © 2013 Wiley Periodicals, Inc. Complexity 18: 58‐64, 2013

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“…Lemma 1 the Young relation [81][82][83] Given constant matrices X and Y with appropriate dimensions and any positive symmetric matrix M , the following inequality holds:…”

Section: Preliminary Lemmasmentioning

confidence: 99%

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

et al. 2017

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This paper deals with the tracking approach of a self-generated stable limit cycle for an underactuated mechanical system: The Inertia Wheel Inverted Pendulum (IWIP). Such system is subject to unilateral constraints limiting its swing motion. It is known that an Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) can be employed to control such pendulum to its upright position. In this work, we briefly show first that the IWIP can generate a stable period-1 limit cycle through a Hopf bifurcation by varying some gain parameter of the IDA-PBC. Thus, such self-generated limit cycle is used as a reference trajectory, which is chosen to be tracked by the IWIP. To achieve the tracking problem, a supplementary control input is added. Such tracking problem is reformulated as an asymptotic stabilization of the tracking error. Our fundamental approach hinges mainly on the use of the S-procedure to introduce the unilateral constraints, and the Schur complement and the matrix inversion lemma to transform Bilinear Matrix Inequalities (BMI) into Linear Matrix Inequalities (LMI). Several simulations have been presented to corroborate the mathematical results and to show the efficiency of the proposed tracking scheme of the self-generated stable limit cycle of the controlled IWIP, even if it is subject to external disturbances, or in the presence of uncertainties in the friction parameters.

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An LMI approach to robust synchronization of a class of chaotic systems with gain variations

Cited by 19 publications

References 11 publications

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

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