论文标题
关于无限维港口港口系统的狄拉克结构
On Dirac structure of infinite-dimensional stochastic port-Hamiltonian systems
论文作者
论文摘要
考虑了带有乘型高斯白噪声的随机无限量 - 港口港口系统（SPHSS）。在本文中，我们通过添加一些额外的随机端口，将确定性分布式参数港口系统的狄拉克结构的概念扩展到随机端口。使用随机积分的Stratonovich形式主义，事实证明，SPHSS的端口的扩展互连仍会形成狄拉克结构。这构成了我们的主要贡献。然后，我们推断出（随机）狄拉克结构之间的互连再次是某些假设下的（随机）狄拉克结构。这些互连结果应用于由带有外部输入和输出的质量弹簧系统在边界上驱动的随机振动字符串组成的系统。这项工作是由SPHSS边界控制问题的动机，并将成为发展稳定方法的基础。
Stochastic infinite-dimensional port-Hamiltonian systems (SPHSs) with multiplicative Gaussian white noise are considered. In this article we extend the notion of Dirac structure for deterministic distributed parameter port-Hamiltonian systems to a stochastic ones by adding some additional stochastic ports. Using the Stratonovich formalism of the stochastic integral, the proposed extended interconnection of ports for SPHSs is proved to still form a Dirac structure. This constitutes our main contribution. We then deduce that the interconnection between (stochastic) Dirac structures is again a (stochastic) Dirac structure under some assumptions. These interconnection results are applied on a system composed of a stochastic vibrating string actuated at the boundary by a mass-spring system with external input and output. This work is motivated by the problem of boundary control of SPHSs and will serve as a foundation to the development of stabilizing methods.
