Physics-informed Koopman learning approach for fixed-time synchronization of stochastic neural dynamics

This study proposes a physics-informed Koopman operator framework for the fixed-time (FXT) synchronization of Hindmarsh-Rose (HR) neurons subject to mixed Gaussian and Poisson jump noise. This paper introduces the Koopman operator to lift the nonlinear neuronal dynamics into a higher dimensional space where the evolution becomes globally linear. Distinct to the data-driven methods which rely on genric basis functions, this paper design a physics-informed lifting dictionary explicitly derived from the governing algebraic nonlinearities of the HR dynamics. Based on the proposed lifted framework, this study designs a non-singular FXT controller which guarantees the convergence within a pre-determined settling time, independent of the initial error states. Further, the communication bandwidth limitations are handled through a dynamic event-triggering mechanism (DETM) ensuring the control actions are executed only when the event-triggering condition is satisfied. The numerical simulations are performed to validate the performance of the proposed theoretical frameworks.