Unbounded Observers and Riccati Operators in Nonreflexive Spaces

Abstract

An infinite horizon linear quadratic optimal control problem in a (nonreflexive) Banach space is considered. The control and observation operators are unbounded (the control operator has range in the extrapolated Favard class, the observation operator is defined on the Favard class). We prove the existence of the Riccati operator synthetizing the optimal solution in the feedback form, describing the value functional and satisfying the algebraic Riccati equation (we also prove that it is the minimal positive solution of the Riccati equation).