对于具有倍增噪声和部门类型非线性系统的随机反共振
Adrian-Mihail Stoica1, Isaac Yaesh2
1Faculty of Aerospace Engineering, University Politehnica of Bucharest, 060042 Bucharest, Romania.
Entropy (Basel, Switzerland)
|February 23, 2024
概括
随机反共振可以使用状态乘法噪声稳定不稳定的非线性系统. 这种在工程和生物学中适用的方法利用噪音来控制混乱的行为.
科学领域:
- 非线性动力学和控制系统
- 随机系统分析 随机系统分析
- 应用数学 应用数学 应用数学
背景情况:
- 在工程,物理学和生物学中,具有板块边界非线性性的非线性系统很普遍.
- 在没有噪音的情况下,这些系统可能表现出不稳定或混乱的行为.
- 使用神经网络的近似方法,如霍普菲尔德网络,也存在类似的动态挑战.
研究的目的:
- 研究用于稳定非线性系统的随机反共振的应用.
- 为了证明状态乘数噪声可以用来稳定没有噪声不稳定的系统.
- 开发噪声诱导稳定理论条件.
主要方法:
- 考虑非线性系统的随机反共振,而非线性系统的非线性取决于行业.
- 使用线性矩阵不等式 (LMI) 技术推导稳定条件.
- 用一个新的非二次的Lyapunov函数来进行稳定性分析.
主要成果:
- 它表明,特定水平的状态乘数噪声可以稳定其他不稳定的非线性系统.
- 基于线性矩阵不等式的稳定条件得到了推导.
- 一个数值示例展示了一个混乱的非线性系统使用状态乘法噪声的稳定.
结论:
- 状态倍增噪声为稳定不稳定的非线性系统提供了一个可行的机制.
- 开发的基于LMI的条件为设计噪声诱导稳定策略提供了严格的框架.
- 随机反共振是一种强大的范式,用于控制复杂的非线性动态.
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