不连续驱动-响应网络的固定与预定时间同步

Fixed and preassigned-time synchronization of drive-response networks with discontinuous activation functions

研究具有不连续激活函数的驱动-响应网络固定时间与预定时间同步问题.针对不连续系统,通过比较原理和变量代换推导更精确的固定时间稳定性定理,并设计不含线性项的固定时间同步控制器与控制增益有限的预定时间同步控制器.基于所提出的定理与控制器,结合不连续微分方程理论,分别得到实现网络固定时间同步与预定时间同步的充分条件.预定同步时间可根据实际情况预先指定,与系统初始值及控制器参数无关.数值模拟结果验证了稳定性定理的正确性与同步时间估计的准确性.

Aiming at the problem of fixed and preassigned-time synchronization of drive-response networks with discontinuous activation function, we derive a fixed-time stability theorem with more accurate stable time estimation for discontinuous systems by comparison principle and variable substitution. We design a fixed-time synchronization controller without linear term and a preassigned-time synchronization controller with limited control gain. Based on the proposed theorem and controller, together with the theory of discontinuous differential equations, we obtain the sufficient conditions for realizing fixed-time synchronization of drive-response networks with discontinuous activation function, and the sufficient condition for realizing the preassigned-time synchronization of drive-response networks with discontinuous activation function. Wherein, the synchronization time can be prespecified according to the actual situation, and it is independent of the initial value of the system and the controller parameters. The numerical simulation results verify the correctness of the stability theorem and the accuracy of the synchronization time estimation.