Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach

Chen, Chaio-Shiung; Chen, Heng-Hui

doi:10.1007/s11071-010-9794-3

Cited by 8 publications

(3 citation statements)

References 30 publications

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“…In , a simple linear feedback controller is proposed to make the states of two identical unified chaotic systems asymptotically synchronized. In , using a four‐layered fuzzy neural network identifier, an LMI‐based intelligent quadratic optimal controller is suggested for the synchronization of uncertain chaotic systems with external disturbances and parametric uncertainties. In , the chaos synchronization problem of general chaotic systems is studied which satisfies the Lipschitz condition with uncertain variables via linear coupling and pragmatical adaptive tracking.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Mobayen

Tchier

2017

Asian Journal of Control

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This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

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Section: Introductionmentioning

confidence: 99%

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Mobayen

Tchier

2017

Asian Journal of Control

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“…If these methods prove stability in the general case, they will also be valid for special (chaotic) systems. Adaptive control [11], sliding mode control [12], neural network control [13], fuzzy control [14], and robust control [15] are also in this category. Fradkov and Evans [16] examined various methods of controlling chaos and studied their applications in engineering.…”

Section: Introductionmentioning

confidence: 99%

Robust H$\infty $ control for chaotic supply chain networks

Nav¹,

Jahed‐Motlagh²,

Makui³

2017

Turk J Elec Eng & Comp Sci

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Abstract:A supply chain network (SCN) is a complex nonlinear system involving multiple entities. The policy of each entity in decision-making and the uncertainties of demand and supply (or production) significantly affect the complexity of its behavior. Although several studies have presented information about the measurement of chaos in the supply chain, there has not been an appropriate way to control the chaos in it. In this paper, the chaos control problem is considered for a SCN with a time-varying delay between its entities. The innovation of this paper is the more comprehensive modeling, analysis, and control of chaotic behavior in the system. The proposed model has a control center to determine the orders of entities and control their inventories. Customer demand is modeled as an unknown exogenous disturbance. A robust H ∞ control method is designed to control its chaotic behavior in terms of a certain linear matrix inequality technique that can be readily solved using the MATLAB LMI toolbox. By using this technique and calculating the maximum Lyapunov exponent, decision parameters are determined in such a way that the behavior of the SCN is stable.

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“…Fuzzy control has also been applied to stabilizing chaotic systems since the Takagi-Sugeno (T-S) fuzzy model can express a chaotic system with a small number of applications of rules (Vembarasan and Balasubramaniam, 2013;Xie et al 2013). Linear matrix inequality (LMI), as a very important and classic tool, has been widely used in the fuzzy control of integer-order chaos (Chen, 2010;Chen and Chen, 2011;Chadli and Guerra, 2012;Wang et al, 2012;Chesi, 2013;Faieghi et al, 2013). However, the stability region of fractional-order chaos is different with integer-order chaos.…”

Section: Introductionmentioning

confidence: 99%

Takagi-Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality

Wang

Xue

Chen

2014

Journal of Vibration and Control

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In this paper, the authors focus on the application of linear matrix inequality (LMI) in the stabilization of fractional-order chaotic systems and the strict mathematical description and proof of LMI. Based on the theory of the fractional-order interval system, the generalized Takagi-Sugeno fuzzy model is applied to a wide class of fractional-order chaotic systems with uncertain parameters. The sufficient stability condition for the fractional-order systems is presented as a set of LMI for the first time and the strict mathematical norms of LMI are given. Furthermore, a controller is developed to stabilize fractional-order chaotic systems, and may be applied to fractional-order systems with uncertainty. Finally, two representative examples of the three-dimensional fractional-order permanent magnet synchronous motor system and the four-dimensional fractional-order hyperchaotic system based on Chen’s system are provided to demonstrate the effectiveness of theoretical analysis.

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Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach

Cited by 8 publications

References 30 publications

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Robust H$\infty $ control for chaotic supply chain networks

Takagi-Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality

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