2013
DOI: 10.1137/120867433
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A Theory of the Infinite Horizon LQ-Problem for Composite Systems of PDEs with Boundary Control

Abstract: We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall 'predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control action… Show more

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Cited by 12 publications
(96 citation statements)
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“…(This is again a consequence of the fact that [14, Lemma 2.4] is here replaced by Proposition 2.4.) On the other hand, we seek to disclose the improved (space) regularity (1.7), even though for the purpose of invoking the theory in [1,3] the membership L q (0, T ; L 2 (Γ s )) in (1.8) would suffice. A shared tool for both proofs is interpolation, and more specifically a result which also involves the dual of Sobolev spaces with fractional exponents (see [35,Theorem 12.5]).…”
Section: )mentioning
confidence: 99%
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“…(This is again a consequence of the fact that [14, Lemma 2.4] is here replaced by Proposition 2.4.) On the other hand, we seek to disclose the improved (space) regularity (1.7), even though for the purpose of invoking the theory in [1,3] the membership L q (0, T ; L 2 (Γ s )) in (1.8) would suffice. A shared tool for both proofs is interpolation, and more specifically a result which also involves the dual of Sobolev spaces with fractional exponents (see [35,Theorem 12.5]).…”
Section: )mentioning
confidence: 99%
“…The obtained results, collectively stated as Theorem 1.2 in Section 1.2 below, are central to solvability of the associated optimal control problems with quadratic functionals; see Section 3, in particular Remark 3.1 and the subsequent verification. To be more specific, Theorem 1.2 attests the applicability of the Linear-Quadratic (LQ) theory on an infinite time horizon devised by Acquistapace, Lasiecka and this author in [3]. This theory, tailored to coupled PDE systems which comprise both hyperbolic and parabolic components, with the latter subject to boundary/interface control, finds in (1.1) a significant FSI illustration, besides and beyond relevant physical interactions such as mechanical-thermal (and acoustic-structure) ones, which provided its original motivation.…”
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confidence: 94%
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“…And, further, appropriate regularity properties can be displayed by certain coupled systems of hyperbolic-parabolic PDE's subject to boundary control -including thermoelastic systems, acoustic-structure and fluidstructure interactions -, which ensure the solvability of the associated optimal control problems (with quadratic functionals), along with well-posed Riccati equations. The ultimate finite and infinite time horizon theories, as well as references to the motivating PDE systems, are found respectively in [1] and [2]. )Returning to the PDE under investigation, as we know from [29] and [21], the…”
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confidence: 99%