Classical Solutions of Nonautonomous Riccati Equations Arising in Parabolic Boundary Control Problems

Classical Solutions of Nonautonomous Riccati Equations Arising in Parabolic Boundary Control... An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential Riccati equation is studied from the point of view of semigroup theory; it is shown to have a classical, explicitly represented solution for very general final data; weighted Hölder regularity results for the optimal pair are deduced. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Classical Solutions of Nonautonomous Riccati Equations Arising in Parabolic Boundary Control Problems

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 1999 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900111
Publisher site
See Article on Publisher Site

Abstract

An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential Riccati equation is studied from the point of view of semigroup theory; it is shown to have a classical, explicitly represented solution for very general final data; weighted Hölder regularity results for the optimal pair are deduced.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 1, 2041

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