Constrained optimal boundary state estimation for dissipative systems

The main purpose of this paper is the development of a constrained optimal boundary state estimation framework for the dissipative systems with boundary control and boundary observation operator. These dissipative systems will be described by an extended system which involves no unbounded operator except for the system´s dynamics generator through the change of variables and Yosida approximation. Then, the constrained optimal state estimation problem is posed for the resulting extended system and the original system as well. Finally, an important and practically significant realization of constraints embedded in the structure of the optimal filter is realized. In addition, the explanation is provided as to how constraints fit in the optimal filter structure.