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，我们考虑了随机两相Stefan系统的状态和自由边界估计问题。首先，通过在时间和空间变量方面使用有限差异方法讨论了对状态方程的解决方程的存在和唯一性能。其次，通过使用martingale代表理论得出状态和自由边界估计器动力学。最后，显示了通过数字仿真实验获得的代表性样本运行，包括一种简单的近似方法来实现非线性估计器动力学2。在随机分布式参数系统的状态和自由边界估计上：这项研究涉及具有障碍的随机分布式参数系统的状态和自由边界估计问题。通过使用惩罚方法研究了将系统模型作为随机变异不平等的形式，解决方案的存在和唯一性能。无状态边界估计器的动力学是在分布式噪声观察下给出的。为了支持此处开发的理论方面，显示了一个说明性示例，包括数字仿真实验的结果。