Finite-Time pth Moment Asymptotically Bounded for Stochastic Nonlinear Systems and Its Application in Neural Networks Synchronization
研究了随机非线性系统在有限时间内的p阶矩渐近有界性，并应用于随机神经网络的p阶矩准同步，给出了同步条件并分析了参数对能耗的影响。
This article pays attention to finite-time (FnT) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> th moment asymptotically bounded (MAB) for stochastic nonlinear systems (SNSs) and its application to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> th moment quasi-synchronization (MQS) of stochastic neural networks (SNNs) based on parameter mismatches. First, this article develops FnT asymptotically bounded theorems SNSs. In detail, several new FnT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> th MAB theorems of the SNSs are proposed, the mathematical expression of finite settlement time is obtained, and the bounds of MAB are estimated. Second, new sufficient conditions are designed to ensure FnT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> th MQS of SNNs. In particular, novel FnT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> th MQS conditions of the SNNs enlarge the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> . Moreover, when the initial value of the system meets certain conditions, the smaller the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> is, the smaller the system synchronization control energy consumption is, which can be more meaningful. Finally, a numeric example illustrates the validity of the methods.