In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.

This paper addresses the problem of observer-based adaptive sliding mode control (SMC) for nonlinear Markov jump systems (MJSs), using a Takagi-Sugeno (T-S) fuzzy model with the premise variables of fuzzy rules depend on system state. Firstly, an integral sliding surface is designed based on fuzzy observer system; Secondly, sufficient conditions for stochastic stability and $ H_{\infty} $ perturbation attenuate level are provided for the obtained sliding mode dynamics and error systems using linear matrix inequality techniques. Furthermore, an adaptive SMC law is combined with the observed state variables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.

研究了激光Maxwell-Bloch 方程时空混沌网络的同步问题.对单模激光Maxwell-Bloch方程进行了修正. 以N个修正后具有时空混沌特性的单模激光Maxwell-Bloch方程作为网络节点构成复杂网络. 在考虑到网络连接过程中,节点时空混沌系统中的参量可能受到某种干扰而与实际值产生微小偏差的情况下,采用网络第一个节点的时空混沌系统同时并行驱动其余N-1个时空混沌系统达到同步. 进一步通过仿真模拟验证了同步方案的有效性.