Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
From MaRDI portal
Publication:4744144
DOI10.1137/0321003zbMath0506.93036OpenAlexW4252456749MaRDI QIDQ4744144
Roberto Triggiani, Irena Lasiecka
Publication date: 1983
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0321003
Control/observation systems governed by partial differential equations (93C20) Initial-boundary value problems for second-order parabolic equations (35K20) Synthesis problems (93B50) Groups and semigroups of linear operators (47D03) Existence theories for optimal control problems involving partial differential equations (49J20) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)
Related Items (37)
Riccati equations for nonsymmetric and nondissipative hyperbolic systems with \(L_ 2\)-boundary controls ⋮ A direct study of the Riccati equation arising in hyperbolic boundary control problems ⋮ Direct solution of a Riccati equation arising in a stochastic control problem with control and observation on the boundary ⋮ On the direct solution of Riccati equations arising in boundary control theory ⋮ Invertibility of Riccati operators and controllability of related systems ⋮ Infinite-horizon boundary control of distributed systems ⋮ Input dynamics and nonstandard Riccati equations with applications to boundary control of damped wave and plate equations ⋮ Riccati equation arising in the boundary control of stochastic hyperbolic systems ⋮ The regulator problem for parabolic equations with Dirichlet boundary control. I: Riccati's feedback synthesis and regularity of optimal solution ⋮ Filtering and controal of stochastic differential equations with unbounded coefficients ⋮ The regulator problem for parabolic equations with Dirichlet boundary control. II: Galerkin approximation ⋮ On nonlinear Miyadera-Voigt perturbations ⋮ Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement ⋮ Differential Riccati equations with unbounded coefficients: applications to boundary control/boundary observation hyperbolic problems ⋮ Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems ⋮ Maximal controllability for boundary control problems ⋮ Mild solution and constrained local controllability of semilinear boundary control systems ⋮ The Nehari problem for infinite-dimensional linear systems of parabolic type ⋮ Approximations of riccati equation for abstract boundary control problems applications to hyperbolic systems ⋮ Boundary feedback control of the Burgers equations by a reduced-order approach using centroidal Voronoi tessellations ⋮ Global regularity and stability analysis of the Patlak-Keller-Segel system with flow advection in a bounded domain: a semigroup approach ⋮ Differentiability with respect to (t,s) of the parabolic evolution operator ⋮ A new proof of an a priori estimate arising in boundary control theory ⋮ Dynamical reconstruction of inputs for contraction semigroup systems: Boundary input case ⋮ Global existence for an abstract Riccati initial-value problem with possibly unbounded coefficients ⋮ Numerical Approximations of Algebraic Riccati Equations for Abstract Systems Modelled by Analytic Semigroups, and Applications ⋮ Covergence rates for the approximations of the solutions to algebraic Riccati equations with unbounded coefficients: Case of analytic semigroups ⋮ Abstract settings for tangential boundary stabilization of Navier--Stokes equations by high- and low-gain feedback controllers. ⋮ Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation ⋮ Finite-dimensional VS-MRAC of distributed parameter systems with boundary inputs ⋮ Unnamed Item ⋮ A counterexample in the boundary control of parabolic systems ⋮ Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data ⋮ Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data ⋮ Optimal boundary control of the heat equation with target function at terminal time. ⋮ Feedback exact null controllability for unbounded control problems in Hilbert space ⋮ Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems -- strong convergence of optimal controls
This page was built for publication: Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
