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Stochastic state estimation for neural networks with distributed delays and Markovian jump. 2012

Yun Chen, and Wei Xing Zheng
Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China.

This paper investigates the problem of state estimation for Markovian jump Hopfield neural networks (MJHNNs) with discrete and distributed delays. The MJHNN model, whose neuron activation function and nonlinear perturbation of the measurement equation satisfy sector-bounded conditions, is first considered and it is more general than those models studied in the literature. An estimator that guarantees the mean-square exponential stability of the corresponding error state system is designed. Moreover, a mean-square exponential stability condition for MJHNNs with delays is presented. The results are dependent upon both discrete and distributed delays. More importantly, all of the model transformations, cross-terms bounding techniques and free additional matrix variables are avoided in the derivation, so the results obtained have less conservatism and simpler formulations than the existing ones. Numerical examples are given which demonstrate the validity of the theoretical results.

UI MeSH Term Description Entries
D008390 Markov Chains A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system. Markov Process,Markov Chain,Chain, Markov,Chains, Markov,Markov Processes,Process, Markov,Processes, Markov
D013269 Stochastic Processes Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables. Process, Stochastic,Stochastic Process,Processes, Stochastic
D013997 Time Factors Elements of limited time intervals, contributing to particular results or situations. Time Series,Factor, Time,Time Factor
D016571 Neural Networks, Computer A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming. Computational Neural Networks,Connectionist Models,Models, Neural Network,Neural Network Models,Neural Networks (Computer),Perceptrons,Computational Neural Network,Computer Neural Network,Computer Neural Networks,Connectionist Model,Model, Connectionist,Model, Neural Network,Models, Connectionist,Network Model, Neural,Network Models, Neural,Network, Computational Neural,Network, Computer Neural,Network, Neural (Computer),Networks, Computational Neural,Networks, Computer Neural,Networks, Neural (Computer),Neural Network (Computer),Neural Network Model,Neural Network, Computational,Neural Network, Computer,Neural Networks, Computational,Perceptron

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