A Bolza optimal synthesis problem for singular estimate control systems

• Autorzy: Lasiecka I. , Tuffaha A.
• Języki publikacji: EN

Abstrakty

EN

Bolza problem governed by PDE control systems with unbounded controls is considered. The motivating example is fluid structure interaction model with boundary-interface controls. The aim of the work is to provide optimal feedback synthesis associated with well denned gain operator constructed from the Riccati equation. The dynamics considered is of mixed parabolic-hyperbolic type which prevents applicability of tools developed earlier for analytic semigroups. It is shown, however, that the control operator along with the generator of the semigroup under consideration satisfy singular estimate referred to as Revisited Singular Estimate (RSE). This estimate, which measures "unboundedness" of control actions, is a generalization and a weaker form of Singular Estimate (SE) treated in the past literature. The main result of the paper provides Riccati theory developed for this new class of control systems labeled as RSECS (Revisited Singular Estimate Control Systems). The important feature is that the gain operator, constructed via Riccati operator, is consistent with the optimal feedback synthesis. The gain operator, though unbounded, has a controlled algebraically singularity at the terminal point. This enables one to establish well-posedness of the Riccati solutions and of the optimal feedback representation. An application of the theoretical framework to boundary control of a fluid-structure interaction model is given.

Słowa kluczowe

EN

Bolza problem; Riccati equation; singular estimate control systems; fluid-structure interaction

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4B
• Strony: 1429--1460
• Opis fizyczny: Bibliogr. 42 poz.

Twórcy

autor

Lasiecka I.

autor

Tuffaha A.

• Department of Mathematics, University of Virginia Charlottesville, VA 22901, USA

Bibliografia

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