Boundary Control Systems with Yosida Type Approximate Boundary Observation

A model of boundary control system with boundary observation is described and analyzed, which involves no unbounded operator except for the dynamics generator. This model consists of an extended abstract differential equation whose state components are the boundary input, the state (up to an affine transformation) and a Yosida-type approximation of the output of the nominal system. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of an analytic C0-semigroup and the model is observable. Moreover the model is shown to be approximately reachable provided that so is the nominal system with respect to an additional distributed input. It is expected that this approach will lead hopefully to a good trade-off between the cost of modelling and the efficiency of methods of resolution of control problems for such systems.