Approximate moment dynamics for polynomial and trigonometric stochastic systems
Approximate moment dynamics for polynomial and trigonometric stochastic systems
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DOI：
10.1109/cdc.2017.8263922
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发表时间：
2017-03
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影响因子：
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通讯作者：
K. Ghusinga;Mohammad Soltani;Andrew G. Lamperski;S. Dhople;Abhyudai Singh
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作者：
K. Ghusinga;Mohammad Soltani;Andrew G. Lamperski;S. Dhople;Abhyudai Singh
随机动力系统通常包含非线性，这使得难以计算这些系统的概率密度函数或统计矩。对于力矩计算，非线性导致众所周知的未闭合力矩动力学问题，即，控制直到某一阶的力矩的时间演化的微分方程可能包含一些更高阶的力矩。矩闭合技术被用来找到一个近似的，封闭的系统方程的时刻动态，但其使用是相当有限的系统与连续状态，特别是当非线性是非多项式。在这里，我们扩展了基于导数匹配的矩封闭技术，这是最初提出的多项式随机系统的离散状态，连续状态随机微分方程的多项式和三角非线性。
Stochastic dynamical systems often contain non-linearities that make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities lead to the well-known problem of unclosed moment dynamics, i.e., differential equations that govern the time evolution of moments up to a certain order may contain some moments of higher order. Moment closure techniques are used to find an approximate, closed system of equations for the moment dynamics, but their usage is rather limited for systems with continuous states particularly when the nonlinearities are non-polynomials. Here, we extend a moment closure technique based on derivative matching, which was originally proposed for polynomial stochastic systems with discrete states, to continuous state stochastic differential equations with both polynomial and trigonometric nonlinearities.