Observers and parameter determination for distributed parameter systems

The aim of the paper is to investigate the estimation of unknown states and unknown functions for distributed parameter systems. First we construct finite dimensional state observers to estimate the unknown states and give the error estimates for the distributed parameter systems of parabolic type with unknown input sources. Next we consider the determination of unknown input distribution functions using these estimated states. The problems of unknown function determination are not necessarily well-posed even if the distributed parameter systems are identifiable. A well-posed approximation method by regularization is applied to obtain the approximate functions which depend continuously on the measurement data. We also construct finite dimensional state observers for the distributed parameter systems of hyperbolic type with unknown input sources. Simple numerical examples are presented.