无界时滞八元数神经网络的全局$μ$稳定性与有限时间控制
Global $μ$-stability and finite-time control of octonion-valued neural networks with unbounded delays
摘要：
八元数值神经网络（OVNN）是一种状态和权重都是八元数的神经网络。研究了具有无界异步时变时滞的八元数神经网络的全局$μ$稳定性和有限时间稳定性问题。为了避免八元数的非通信和非联想乘法特性，我们首先将OVNN等价地分解为八个实值神经网络（RVNN）。利用广义范数和Cauchy收敛原理，得到了OVNN平衡点存在唯一性和全局$μ$-稳定性的充分判据.通过增加控制器，将有限时间稳定性分析过程分为两个阶段，给出了保证OVNN有限时间稳定性的判据。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。最后给出了具体算例的仿真结果，验证了理论结果的有效性和正确性。
英文摘要：
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.
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