This article concentrates on the finite-time synchronization (FTS) for multi-weighted fractional-order coupled neural networks (MFCNNs) with fixed and adaptive couplings. A new dynamic model, which involves coupled neural networks with fractional order and multi-weighted couplings, is proposed. Furthermore, an adaptive law to adjust the coupling weights is devised to ensure the FTS of such a complex model. First, by using fractional-order calculus properties and inequality techniques, a finite-time fractional differential inequality is presented, which considerably extends the prior result. Second, by the Lyapunov stability theory and the fractional-order inequality, several sufficient conditions are acquired to make sure the FTS for MFCNNs. Moreover, the influence of the system's order on the FTS is also uncovered. Finally, a numerical simulation example and a practical simulation example are provided to demonstrate the validity of the obtained criteria.

This article reports on exponential synchronization for stochastic coupled neural networks (NNs) with mixed time‐varying delays, stochastic coupling strength, and Markovian switching. In order to reduce the amount of data transmission and save network resources, an event‐triggered control method is provided in this study. When the triggered condition can be met, the data can be transmitted so that the master and slave systems with limited resources and bandwidth can realize synchronization. By the Lyapunov stability theory and several analysis skills of matrix properties, some new criteria are obtained to make sure that stochastic coupled NNs are mean square exponential stability. These criteria are provided by linear matrix inequalities. Finally, a numerical case further demonstrates the validity of the proposed criteria.

The optimal guaranteed cost sampled‐data control problem is studied for high‐speed train systems. To keep the relative speed and relative displacement of each high‐speed train stable, and ensure the performance level of high‐speed trains at the same time, sufficient conditions are obtained for the optimal guaranteed cost sampled‐data controller of train systems. By the convex optimization method, the minimum upper bound of high‐speed train systems is obtained. At last, two examples are presented to substantiate the correctness of theoretical results.