On the State Estimate for Stochastic Distributed Parameter Systems with Boundary Input

Abstract

The purpose of this paper is to study the state estimate for a class of stochastic distributed parameter systems with the boundary input. First, the mathematical model of the stochastic distributed parameter system is formulated by the stochastic variational inequality in Hilbert space. Applying the regularization method to the stochastic variational inequality, the existence and uniqueness theorems of the solution are established. Secondly, the dynamics of state estimate is given in the sense of minimizing the mean square estimation error bound under a distributed noisy observation. Finally, for the purpose of supporting theoretical aspects developed here, an illustrative example is shown, including results of digital simulation experiments.