Abstract
The aim of this paper is to investigate the problem of initial state determination for discrete-time distributed parameter systems. The discrete-time distributed parameter systems are described by differential-difference or integral-difference equations. The problem of initial state determination for distributed parameter systems is not well-posed in general. That is, an initial state is not uniquely determined from measurement data. The problem of initial state determination is formulated as the problem of minimizing a functional (which measures the error between the observed output and model output) with respect to the unknown initial states. After the problem formulation, the approximation method by regularization is presented and analyzed. It gives uniquely an approximate initial state depending continuously on the measurement data. The convergence of approximate solutions is discussed under the assumption that the system is N output controllable with respect to initial states. The method is demonstrated by giving a simple example for the system with pointwise observation.
