On the state estimates for a class of stochastic distributed parameter systems with a semi-permeable wall

This paper is concerned with the state estimate of a system with a semi-permeable wall modeled by the stochastic partial differential equation of the parabolic type with the partial differential inequality as its boundary condition. With the mathematical formulation of the system and noisy observation models via variational inequality, the state estimator dynamics is derived under the criterion of the least square method, including results of digital simulation experiments.