School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
Neural Netw. 2023 Aug;165:740-754. doi: 10.1016/j.neunet.2023.06.017. Epub 2023 Jun 21.
This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.
本文针对时滞全四元数不连续神经网络，通过非分离方法，研究了具有参数不确定性的预定时投影同步问题。首先，基于已有工作，建立了一个新的预定时稳定性定理。随后，为了实现控制目标，设计了两种新型的简单无抖振四元控制器，一种不含幂律项，另一种含有双曲正切函数。它们与现有的常见幂律控制器和指数控制器不同。第三，根据 Filippov 不连续性理论，并借助四元数不等式技术，获得了一些新的简洁充分准则，以确保所研究的系统通过预定时稳定性理论达到预定时同步。预定时 Settling 时间与系统的任何参数和任何初始值无关，可根据实际任务要求进行预设。特别地，与现有结果不同，所提出的控制方法可以有效地避免抖振现象，并且为了简化，去除了时滞部分。此外，投影系数是通用的四元数，而不是实数或复数，并且扩展了一些先前的相关结果。最后，报告了数值模拟结果，以证实控制策略的有效性、预定时 Settling 时间的优点以及所获得结果的正确性。
