The regulator problem for parabolic equations with Dirichlet boundary control. II: Galerkin approximation

DOI10.1007/BF01442191zbMath0652.49026OpenAlexW3160857725MaRDI QIDQ1107103

Roberto Triggiani, Irena Lasiecka

Publication date: 1987

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01442191

zbMATH Keywords

convergencefeedback solutionalgebraic Riccati equationsGalerkin approximationparabolic optimal controlcontrol in Dirichlet boundary conditions

Mathematics Subject Classification ID

Related Items (12)

A sharp result on the exponential operator-norm decay of a family of strongly continuous semigroups ⋮ Stability of infinite-dimensional sampled-data systems ⋮ Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement ⋮ Ergodicity and stability for \((b, l)\)-regularized resolvent operator families ⋮ Maximal space regularity in nonhoomogeneous initial boundary value parabolic problem ⋮ Backstepping synthesis for feedback control of first-order hyperbolic PDEs with spatial-temporal actuation ⋮ Weakly-damped focusing nonlinear Schrödinger equations with Dirichlet control ⋮ Numerical Approximations of Algebraic Riccati Equations for Abstract Systems Modelled by Analytic Semigroups, and Applications ⋮ Boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures ⋮ Uniform stability of a family of resolvent operators in Hilbert spaces ⋮ Stabilizability of infinite-dimensional systems by finite-dimensional controls ⋮ Sparse Grid Approximation of the Riccati Operator for Closed Loop Parabolic Control Problems with Dirichlet Boundary Control

Cites Work

• Non homogeneous boundary value problems for second order hyperbolic operators
• Boundary feedback stabilizability of parabolic equations
• Unified theory for abstract parabolic boundary problems - a semigroup approach
• Extending a theorem of A. M. Liapunov to Hilbert space
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Riccati Equation Arising in a Boundary Control Problem with Distributed Parameters
• The Linear Regulator Problem for Parabolic Systems
• Convergence Estimates for Semidiscrete Approximations of Nonselfadjoint Parabolic Equations
• Stabilization and Structural Assignment of Dirichlet Boundary Feedback Parabolic Equations
• Galerkin Approximations of Abstract Parabolic Boundary Value Problems With Rough Boundary Data-L p Theory
• Differentiability and Convergence Rates of Approximating Semigroups for Retarded Functional Differential Equations
• On Decomposition of Generators
• Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
• Rayleigh‐Ritz‐Galerkin methods for dirichlet's problem using subspaces without boundary conditions
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