Research for State Estimation and Optimal Control of Stochastic Distributed Parameter Systems with Free Boundary

自由边界随机分布参数系统的状态估计与最优控制研究

• 批准号: 60550296
• 负责人: SUNAHARA Yoshifumi
• 金额: $ 1.28万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1984
• 资助国家: 日本
• 起止时间: 1984 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60550296/
• 关键词: stochastic partial differential equation; stochastic variational inequality; Stephan system; free boundary problem; stochastic system theory; function space

1. State and free boundary estimations for stochastic two-phase Stefan systems: In this study, we consider the state and free boundary estimation problems for stochastic two-phase Stefan systems. First, the existence and uniqueness properties of the solution to the state equation with white noise coefficients are discussed by using the finite difference method with respect to time and spatial variables. Secondly, the state and free boundary estimator dynamics are derived by using martingale representation theory. Finally, representative sample runs obtained by digital simulation experiments are shown, including a simple approximation method for realizing non-linear estimator dynamics.2. On the state and free boundary estimations for stochastic distributed parameter systems with obstacle: This study is concerned with the state and free boundary estimation problems for the stochastic distributed parameter systems with obstacle. Formulating the system model as a stochastic variational inequality, the existence and uniqueness properties of the solution are investigated by using the penalization method. The dynamics of state-free boundary estimator is given under a distributed noisy observation. For the purpose of supporting the theoretical aspects developed here, an illustrative example is shown including results of digital simulation experiments.

1.随机两相Stefan系统的状态和自由边界估计：在这项研究中，我们考虑随机两相Stefan系统的状态和自由边界估计问题。首先，利用关于时间和空间变量的有限差分方法，讨论了具有白色噪声系数的状态方程解的存在唯一性。其次，利用鞅表示理论导出了状态和自由边界估计动态。最后，通过数字仿真实验给出了具有代表性的样本运行，包括实现非线性估计动态的简单近似方法.关于带障碍物的随机分布参数系统的状态和自由边界估计：本文研究了带障碍物的随机分布参数系统的状态和自由边界估计问题。将系统模型表示为一个随机变分不等式，利用罚函数法研究了系统解的存在唯一性。在分布噪声观测下，给出了无状态边界估计器的动力学性质。为了支持这里开发的理论方面的目的，一个说明性的例子，包括数字仿真实验的结果。