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

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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.