论文标题
全局$μ$ $稳定性和无限延迟的八元价值神经网络的有限时间控制
Global $μ$-stability and finite-time control of octonion-valued neural networks with unbounded delays
论文作者
论文摘要
八元性神经网络（OVNNS）是一种神经网络，状态和权重为八元。在本文中，在无限制和异步时间变化的延迟下，将全球$ $ $ $稳定性和有限的时间稳定性问题视为被认为是在无限制的和异步的延迟下。为了避免八分元的非交流和非缔合乘法特征，我们首先将OVNN分解为八个实用值的神经网络（RVNN）。通过使用广义规范和库奇收敛原则，我们获得了足够的标准，这些标准可以确保OVNNS的平衡点的存在，平衡点的独特性和全局$μ$稳定性。通过添加控制器，通过将有限时间稳定过程的分析分为两个阶段来确保OVNN的有限时间稳定性的标准。此外，我们还证明了上述网络的自适应有限时间稳定性理论。最后，给出了指定示例的仿真结果，以证实理论结果的有效性和正确性。
Octonion-valued neural networks (OVNNs) are a type of neural networks for which the states and weights are octonions. In this paper, the global $μ$-stability and finite-time stability problems for octonion-valued neural networks are considered under unbounded and asynchronous time-varying delays. To avoid the non-communicative and non-associative multiplication feature of the octonions, we firstly decompose the OVNNs into eight real-valued neural networks (RVNNs) equivalently. Through the use of generalized norm and the Cauchy convergence principle, we obtain the sufficient criteria which assure the existence, uniqueness of the equilibrium point and global $μ$-stability of OVNNs. By adding controllers, the criteria to ensure the finite-time stability for OVNNs are presented by dividing the analysis of finite-time stability process into two phases. Furthermore, we also prove the adaptive finite time stability theory of above networks. At last, the simulation results of specified examples is given to substantiate the effectiveness and correctness of the theoretical results.
