Differential Riccati equation for the active control of a problem in structural acoustics

DOI10.1007/BF02190128zbMath0869.93023WikidataQ115392723 ScholiaQ115392723MaRDI QIDQ2564170

George Avalos, Irena Lasiecka

Publication date: 4 September 1997

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

unbounded operatorRiccati equationfluid-structure interactionhyperbolic-parabolic systemregularity of optimal controlexistence and uniqueness of an optimal controlfluid acousticsstructural elasticity

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Linear-quadratic optimal control problems (49N10) Control/observation systems in abstract spaces (93C25) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (34)

Stabilization of a fluid-structure interaction model ⋮ Improved boundary regularity for a Stokes-Lamé system ⋮ Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions ⋮ The stochastic linear quadratic optimal control problem in Hilbert spaces: a polynomial chaos approach ⋮ Boundary controllability of structural acoustic systems with variable coefficients and curved walls ⋮ Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid-structure interaction ⋮ On the infinitesimal generator of an optimal state semigroup ⋮ Asymptotic solution of the singularly perturbed infinite dimensional Riccati equation ⋮ Exact controllability of structural acoustic interactions ⋮ The stochastic linear quadratic optimal control problem on Hilbert spaces: the case of non-analytic systems ⋮ Optimal convergence rates for Galerkin approximation of operator Riccati equations ⋮ Uniqueness for Riccati equations with application to the optimal boundary control of composite systems of evolutionary partial differential equations ⋮ Exact boundary controllability of the structural acoustic model with variable coefficients ⋮ Analyticity of a multilayer mead-Markus plate ⋮ Inverse problem for structural acoustic interaction ⋮ The Stochastic Linear Quadratic Control Problem with Singular Estimates ⋮ Min-max game theory and nonstandard differential Riccati equations for abstract hyperbolic-like equations ⋮ Pointwise pressure observations of a canonical structural acoustics model ⋮ The fluid-structure interaction model with both control and disturbance at the interface: a game theory problem via an abstract approach ⋮ The critical case of clamped thermoelastic systems with interior point control: Optimal interior and boundary regularity results ⋮ Riccati equations for the Bolza problem arising in boundary/point control problems governed by \(C_{0}\) semigroups satisfying a singular estimate ⋮ A numerical approximation framework for the stochastic linear quadratic regulator on Hilbert spaces ⋮ On a structural acoustic model with interface a Reissner--Mindlin plate or a Timoshenko beam ⋮ Well-posedness of a structural acoustics control model with point observation of the pressure ⋮ Boundary controllability of a coupled wave/Kirchhoff system ⋮ Sharp regularity estimates for solutions of the wave equation and their traces with prescribed Neumann data ⋮ Modelling and optimal control of coupled structural acoustic systems with piezoelectric elements ⋮ Exact Controllability of Structural Acoustic Interactions with Variable Coefficients ⋮ Min-max game theory and non-standard differential Riccati equations under the singular estimate for \(e^{At}B\) and \(e^{At}G\) in the absence of analyticity ⋮ Riccati equations for generalized singular estimate control systems ⋮ A trace regularity result for thermoelastic equations with application to optimal boundary control ⋮ Uniform stability for solutions of a structural acoustics PDE model with no added dissipative feedback ⋮ Synthesis of finite-dimensional Riccati-based feedback controls for problems arising in structural acoustics ⋮ Asymptotic behaviour of nonlinear structural acoustic interactions with thermal effects on the interface

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