On stochastic observability and controllability for nonlinear distributed parameter systems

The object of this paper is to show sufficient conditions of stochastic observability and controllability for nonlinear distributed parameter systems. The mathematical model considered here is first introduced in the form of nonlinear partial differential equations. The mathematical aspect of the existence and uniqueness of the solution is then developed. Precise definitions of both stochastic observability and controllability are given. Based on the definitions, several theorems are stated, giving sufficient conditions for stochastic observability and controllability in the framework of functional analysis. Finally, comparative discussions between observability and controllability are developed. Applications of the general theory presented here to a class of diffusion systems, including the derivation of concrete forms of sufficient conditions, are also given.