Shin-ichi Aihara

A method for parameter estimation of a class of non-linear distributed systems under noisy observations

Abstract A method is presented for estimating an unknown parameter of a distributed parameter system which depends on the system state. The system considered is modelled by a class of non-linear partial differential equations of a parabolic type. Noisy observations are assumed to be taken through an arbitrary number of sensors allocated on the spatial region. First, the explicit form of the stationary solution of the state equation is discussed. Second, use is made of the maximum likelihood approach to obtain the optimal estimate of the unknown parameter. Consistency properties w.p.1 of the optimal estimate obtained are also shown. Finally, results of digital simulation experiments are included to support the theoretical aspects.

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.

Identification of Boundary Parameter for a Class of Stochastic Infinite Domensional Systems

Abstract Identification of boundary parameter process determined by a certain nonlinear differential equation is considered. Motivated by systems of percolation and electropaint processes, the considered system is assumed to be governed by the Cauchy-Kowaleska type equation with stochastic boundary inputs and certain nonlinearity on the boundary condition. The necessary condition for the optimal maximum-likelihood estimate under noisy partial observations is derived with showing the practical numerical algorithm.

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.