The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

Part I of this paper deals with the problem of designing a feedback control for a linear infinite dimensional system in such a way that a given quadratic cost functional is minimized. The essential feature of this work is that a it allows for unbounded control and observation, i.e. boundary control, point observation, inputoutput delays and b the general theory is presented in such a way that it applies to both parabolic and hyperbolic partial differential equations as well as retarded and neutral functional differential equations. Part II develops a state space approach for retarded systems with delays in both input and output. A particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations fit into the framework of Part I. Author