Differential and Integral Equations

Riccati operators in non-reflexive spaces

Wolfgang Desch, Eva Fašanga, Jaroslav Milota, and Wilhelm Schappacher

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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.

Article information

Differential Integral Equations, Volume 15, Number 12 (2002), 1493-1510.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49N10: Linear-quadratic problems
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N70: Applications in systems theory, circuits, and control theory 49K27: Problems in abstract spaces [See also 90C48, 93C25]


Desch, Wolfgang; Schappacher, Wilhelm; Fašanga, Eva; Milota, Jaroslav. Riccati operators in non-reflexive spaces. Differential Integral Equations 15 (2002), no. 12, 1493--1510. https://projecteuclid.org/euclid.die/1356060709

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