Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality

Guoqiang Tan, Zhanshan Wang

2021IEEE Transactions on Neural Networks and Learning Systems84 citationsDOI

Abstract

This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Topics & Concepts

JumpSet (abstract data type)Regular polygonArtificial neural networkEllipsoidBounded functionMathematicsConvex combinationMarkov processControl theory (sociology)Computer scienceApplied mathematicsMathematical optimizationConvex optimizationMathematical analysisArtificial intelligenceStatisticsControl (management)PhysicsGeometryQuantum mechanicsProgramming languageAstronomyNeural Networks Stability and SynchronizationStability and Control of Uncertain SystemsControl Systems and Identification