Synchronization of Fuzzy Inertial Neural Networks with Time-Varying Delays via Fixed-Time and Preassigned-Time Control

This paper designs a unified control framework to achieve the fixed-time and preassigned-time synchronization of fuzzy inertial neural networks (FINNs) with time-varying delays. First of all, by using the generalized variable transformation, the FINNs model defined by a second-order equation is reduced to two first-order equations. Then, the influence of the fuzzy operations and time delays is offset by devising a proper scaling term. Moreover, by constructing appropriate Lyapunov functions and applying the mean inequality technique, several sufficient conditions are derived to ensure the fixed-time and preassigned-time synchronization for the discussed FINNs. As a result, several more accurate estimations for the settling time are obtained by means of some special functions. Finally, numerical examples are given to show the correctness of the results.