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<i>H</i> <sub>∞</sub> State Estimation for Neural Networks With General Activation Function and Mixed Time-Varying Delays

Wei Qian, Weiwei Xing, Shumin Fei

2020IEEE Transactions on Neural Networks and Learning Systems140 citationsDOI

Abstract

This article deals with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state estimation of neural networks with mixed delays. In order to make full use of delay information, novel delay-product Lyapunov-Krasovskii functional (LKF) by using parameterized delay interval is first constructed. Then, generalized free-weighting-matrix integral inequality is used to estimate the derivative of LKF to reduce the conservatism. Also, a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model. Finally, sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Numerical examples are simulated to show the benefits of our proposed method.

Topics & Concepts

Parameterized complexityEstimatorInterval (graph theory)WeightingControl theory (sociology)MathematicsState estimatorArtificial neural networkActivation functionFunction (biology)Applied mathematicsState (computer science)Derivative (finance)Computer scienceMatrix (chemical analysis)Mathematical optimizationAlgorithmStatisticsCombinatoricsArtificial intelligenceEvolutionary biologyEconomicsMaterials scienceBiologyControl (management)RadiologyFinancial economicsMedicineComposite materialNeural Networks Stability and SynchronizationStability and Control of Uncertain SystemsDistributed Control Multi-Agent Systems
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