Fixed-Time Control and Estimation of Discontinuous Fuzzy Neural Networks: Novel Lyapunov Method of Fixed-Time Stability

Zuowei Cai, Lihong Huang, Zengyun Wang

2023IEEE Transactions on Neural Networks and Learning Systems16 citationsDOI

Abstract

This article considers the fixed-time stability (FXTS) issue for discontinuous system described by differential equation (DE) with time-varying parameters. Using the tool of differential inclusion (DI), several improved FXTS criteria and estimation formulas of settling time (SET) are derived by employing a relaxed Lyapunov method. The special novelty of the developed Lyapunov method is that the derivative of Lyapunov function possesses indefiniteness. As an important application, the established FXTS theorems are utilized to deal with fixed-time (FXT) synchronization issue for fuzzy neural networks (FNNs) possessing state discontinuity, where the fuzzy operation is used in the synaptic law computing, and one typical time-varying switching control protocol is designed. Moreover, a series of estimations of SET for FXT synchronization are given out. Finally, the simulation examples are present to substantiate the validity of the obtained results.

Topics & Concepts

Differential inclusionLyapunov functionControl theory (sociology)MathematicsDiscontinuity (linguistics)Fixed pointSynchronization (alternating current)Artificial neural networkComputer scienceMathematical optimizationControl (management)Topology (electrical circuits)Nonlinear systemArtificial intelligenceMathematical analysisCombinatoricsQuantum mechanicsPhysicsNeural Networks Stability and SynchronizationNeural Networks and ApplicationsDistributed Control Multi-Agent Systems