An optimization-based method for bounding state functionals of nonlinear stochastic systems
An optimization-based method for bounding state functionals of nonlinear stochastic systems
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DOI：
10.1109/cdc.2016.7799088
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
M. Ahmadi;Andreas W. K. Harris;A. Papachristodoulou
中科院分区：
文献类型：
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作者：
M. Ahmadi;Andreas W. K. Harris;A. Papachristodoulou
我们提出了一种用于一类非线性随机微分方程的边界状态泛函的方法。给定一类随机系统的状态泛函，Feynman-Kac 引理是一个描述状态泛函演化的时间倒向偏微分方程。我们基于使用屏障泛函的方法来绑定这些状态泛函。我们证明，在多项式数据的假设下，可以通过使用半定规划来获得界限。然后将所提出的方法应用于遗传负自动调节中的噪声案例研究，以限制二阶矩的函数，这对实验分析特别感兴趣。发现所获得的界限与文献中的实验结果非常吻合。
We propose a method for bounding state functionals of a class of nonlinear stochastic differential equations. Given a class of state functionals of a stochastic system, the Feynman-Kac Lemma is a backward in time partial differential equation that describes the evolution of the state functional. We bound these state functionals based on a method which uses barrier functionals. We show that, under the assumption of polynomial data, the bounds can be obtained by using semi-definite programming. The proposed method is then applied to the case study of noise in genetic negative autoregulation to bound a functional of the second moment, which is of specific interest to experimental assays. The bound obtained is found to be in good agreement with experimental results in the literature.