Optimal adaptive estimation and stochastic control for distributed-parameter systems

The problems of adaptive estimation and control for a general class of linear stochastic partial differential dynamical systems are studied by using the well-known Lainiotis' partition theorem. From the physically realizable point of view, the sensor and interior controller are of pointwise type. As a consequence, it is shown that this theorem leads to a unified treatment of an adaptive control problem under incomplete state informations.