Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Kamel, Mohamed S.; Xia, Youshen

doi:10.1007/s11571-008-9036-2

Cited by 15 publications

(14 citation statements)

References 135 publications

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“…Cohen-Grossberg neural networks model is one of the most popular and typical neural network models. Some other models, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory neural networks, are special cases of the model (Kamel and Xia 2009;Mahdavi and Kurths 2013;Yang et al 2008Yang et al , 2011. Stability and synchronization of continuous Cohen-Grossberg neural networks with or without discrete and distributed delays were studied in the literature (Zhu and Cao 2010;He and Cao 2008;Song and Wang 2008).…”

Section: Introductionmentioning

confidence: 99%

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

2014

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This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The driveresponse set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristorbased neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

2014

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“…Thus, Theorem 2 can guarantee that for any initial point, the proposed CPNN converges globally to x * in a finite time. By comparison, the convergence results of existing neural networks [15][16][17][18][19][20][21][22][23][24]26] and numerical optimization algorithms [3,6−8] could not make sure its convergence. Furthermore, we perform the proposed CPNN, the extended projection neural network (EPNN) and the modified projection type method (MPTM) by Solodov and Tseng [8] :…”

Section: Examplementioning

confidence: 99%

“…By changing some structures of the EPNN, Gao et al [20] presented another cooperative neural network for solving the constrained monotone VI problem (5). The EPNN has lower model complexity than the one given by Gao et al A detail comparison between them can be refereed to a recent literature survey [21] . Recently, following (3), Xia and his coauthors [22,23] developed two cooperative neural network for solving the nonlinear programming problem (6) and the constrained monotone VI problem (5) with linear constraints, and Gao and Liao [24] presented another cooperative neural network for solving the constrained monotone VI problem (5).…”

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confidence: 99%

New cooperative projection neural network for nonlinearly constrained variational inequality

Xia

2009

Sci. China Ser. F-Inf. Sci.

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This paper proposes a new cooperative projection neural network (CPNN), which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints, respectively. Under the monotonicity condition of the corresponding Lagrangian mapping, the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear constraints. Unlike the extended projection neural network, the proposed CPNN has no limitation on the initial point for global convergence. Compared with other related cooperative neural networks and numerical optimization algorithms, the proposed CPNN has a low computational complexity and requires weak convergence conditions. An application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.variational inequality problems, general constraints, cooperative recurrent neural network, complexity, global convergence conditions Constrained optimization problems arise in a wide variety of scientific and engineering applications including signal and image processing, system identification, pattern recognition, optimal control, and so on [1−3] . In many practical applications, related optimization problems are of a timevarying parameter characteristic and thus have to be solved in real time. One example of such applications is the real-time signal processing in wireless communications [4] . Another example is the real-time optimal robot optimal control [5] . For such applications, conventional numerical methods such as the interior-point method [6] , the sequential quadratic programming method [7] , the projection type method [8] , may not be adequate due to the problem complexity and stringent requirement on the computational time. As a software and hardware-implementable approach [9] , recurrent neural networks, including single and cooperative recurrent neural networks, for solving linear and nonlinear constrained optimization problems have been developed in recent decade. By contrast with traditional numerical optimization algorithms, the neural network approach has potential advantages in real-time applications. Moreover, the dynamical analysis techniques with effective

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“…During the past few years, complex networks have become an interesting research topic and appeal to have more attention in different fields from mathematics, biology, engineering sciences (Osborn 2010;Kamel and Xia 2009;Zhang et al 2013e, 2014bWatts and Strogatz 1998;Barabasi and Albert 1999;Zhou et al 2006;Strogatz 2001;Lü and Chen 2005). A complex network is a large set of interconnected nodes, where the nodes and connections can be anything, examples are internet, transportation networks, coupled biological and chemical engineering systems, neural networks in human brains and so on.…”

Section: Introductionmentioning

confidence: 99%

Event-based exponential synchronization of complex networks

2016

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In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed eventtriggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.

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Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Cited by 15 publications

References 135 publications

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

New cooperative projection neural network for nonlinearly constrained variational inequality

Event-based exponential synchronization of complex networks

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