Riccati operators in non-reflexive spaces. (English) Zbl 1011.49021

Summary: We consider a linear quadratic regulator problem in a general Banach space. The control is by an operator with range in the extrapolated Favard class. The observation operator is unbounded. We prove the existence of a Riccati operator which describes the value function for the optimal control and can be used to synthesize optimal feedback, similarly as in Hilbert spaces.


49N10 Linear-quadratic optimal control problems
47D06 One-parameter semigroups and linear evolution equations
49N35 Optimal feedback synthesis