On the State Estimation for Pseudo-Parabolic System with Stochastic Coefficients

The purpose of this paper is to derive the optimal least square state estimator for a class of stochastic pseudo-parabolic systems under noisy observations., First, we are concerned with a study on solution properties of the state equation. Within the framework of function spaces, a rigorous treatment on a class of partial differential equations with stochastic coefficient is demonstrated by showing the existence and uniqueness theorem and, furthermores the regularity theorem for the solution. Secondly, the dynamics of the least square state estimator is given under a distributed observation mechanism. Finally, for the purpose of supporting the theoretical aspects developed here, an example is shown including results of digital simulation experiments.