Robust nonlinear H/sub ∞/ synchronization of chaotic Lur'e systems

Abstract. This paper presents a fuzzy controller to solve a master-slave chaos synchronization problem. At first, the method of traditional sliding mode control is considered, which utilizes the discontinuous sign function to make the system state reaching a sliding surface. Next, fuzzy rules are determined according to the Lyapunov theorem, and the fuzzy controller is designed for chaos synchronization. Finally, an example of chaos synchronization for an uncertain Duffing-Holmes system is presented to illustrate the validity and feasibility of the proposed controller.

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“…In such a case, there are no internal dynamics [11]. Based on the control law proposed by [2], the sliding surface can be defined as…”

Section: Sliding-mode Controlmentioning

confidence: 99%

Design of Fuzzy Sliding-Mode Controller for Chaos Synchronization

Kuo

Shieh

Lin

et al. 2007

Communications in Computer and Information Science

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“…Many approaches and techniques have been proposed for the control of chaos such as OGY method [1], bang-bang control [2], optimal control [3], intelligent control based on neural network [4], feedback linearization [5], differential geometric method [6], adaptive control [7]- [10], H  control method [11], and many others [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Intelligent Backstepping Control for Genesio-Tesi ChaoticSystem Using a Chaotic Particle Swarm OptimizationAlgorithm

Gholipour¹,

Khosravi²,

Mojallali³

2012

IJCEE

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“…Synchronization theory has been intensively studied within the area of chaotic systems and secure communications [Chen & Dong, 1998;Pecora & Carroll, 1990;Suykens et al, 1996Suykens et al, , 1997Suykens et al, , 1998Wu & Chua, 1994]. The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Intelligence and Cooperative Search by Coupled Local Minimizers

Suykens

Vandewalle

Moor

2001

Int. J. Bifurcation Chaos

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We show how coupling of local optimization processes can lead to better solutions than multi-start local optimization consisting of independent runs. This is achieved by minimizing the average energy cost of the ensemble, subject to synchronization constraints between the state vectors of the individual local minimizers. From an augmented Lagrangian which incorporates the synchronization constraints both as soft and hard constraints, a network is derived wherein the local minimizers interact and exchange information through the synchronization constraints. From the viewpoint of neural networks, the array can be considered as a Lagrange programming network for continuous optimization and as a cellular neural network (CNN). The penalty weights associated with the soft state synchronization constraints follow from the solution to a linear program. This expresses that the energy cost of the ensemble should maximally decrease. In this way successful local minimizers can implicitly impose their state to the others through a mechanism of master-slave dynamics resulting into a cooperative search mechanism. Improved information spreading within the ensemble is obtained by applying the concept of small-world networks. We illustrate the new optimization method on two different problems: supervised learning of multilayer perceptrons and optimization of Lennard-Jones clusters. The initial distribution of the local minimizers plays an important role. For the training of multilayer perceptrons this is related to the choice of the prior on the interconnection weights in Bayesian learning methods. Depending on the choice of this initial distribution, coupled local minimizers (CLM) can avoid overfitting and produce good generalization, i.e. reach a state of intelligence. In potential energy surface optimization of Lennard-Jones clusters, this choice is equally important. In this case it can be related to considering a confining potential. This work suggests, in an interdisciplinary context, the importance of information exchange and state synchronization within ensembles, towards issues as evolution, collective behaviour, optimality and intelligence.2

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Robust nonlinear H/sub ∞/ synchronization of chaotic Lur'e systems

Cited by 168 publications

References 24 publications

Design of Fuzzy Sliding-Mode Controller for Chaos Synchronization

Design of Fuzzy Sliding-Mode Controller for Chaos Synchronization

Intelligent Backstepping Control for Genesio-Tesi ChaoticSystem Using a Chaotic Particle Swarm OptimizationAlgorithm

Intelligence and Cooperative Search by Coupled Local Minimizers

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