Stabilization by Artificial Wiener Processes
Stabilization by Artificial Wiener Processes
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DOI：
10.1109/tac.2016.2522087
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发表时间：
2016-01
影响因子：
6.8
通讯作者：
Y. Nishimura
中科院分区：
文献类型：
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作者：
Y. Nishimura
在本技术说明中，我们重新描述了高斯白噪声对连续时间无漂移输入仿射非完整系统的积极影响。与之前的研究相比，我们发现积极的影响隐藏在多维维纳过程上随机积分的非唯一性的阴影之下。此外，我们发现，利用常微分方程的欧拉格式进行数值计算，人为地再现了积极的影响。我们的结果表明，积极影响充当非完整系统的“隐藏的独立控制输入”。这意味着我们的结果为设计控制输入提供了一个建设性的过程，使得原点变得指数级或有限时间稳定的$p$时刻。
In this technical note, we restage the positive effects of Gaussian white noises for continuous-time driftless input-affine nonholonomic systems. Compared with previous studies, we found that the positive effects are hidden in the shadows of nonuniqueness of stochastic integrals over multi-dimensional Wiener processes. Furthermore, we found that the positive effects are artificially restaged by numerical calculations with use of Euler scheme for ordinary differential equations. Our results demonstrate that the positive effects act as “hidden independent control inputs” for nonholonomic systems. This implies that our results provide a constructive procedure for designing control inputs such that the origins become $p$-th moment exponentially or finite-time stable.