A Uniformly Differentiable Approximation Scheme for Delay Systems Using Splines

Abstract

A new spline-based scheme is developed for linear retarded functional differential equations within the framework for semigroups on a certain Hilbert space formula. The approximating semigroups inherit in uniform way the characterization for differentiable semigroups from the solution semigroup of the delay system (e.g., among other things the logarithmic sectorial property for the spectrum). The authors prove convergence of the scheme in state spaces. The uniform differentiability of the approximating semigroups enables us to establish error estimates including quadratic convergence for certain classes of initial data. They also apply the scheme for computing the feedback solutions to linear quadratic optimal control problems.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1989
Accession Number
ADA208567

Entities

People

  • F. Kappel
  • Kazufumi Ito

Organizations

  • Brown University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Banach Space
  • Computations
  • Control Systems
  • Convergence
  • Differential Equations
  • Equations
  • Hilbert Space
  • Inequalities
  • Mathematics
  • Numbers
  • Riccati Equation
  • Security
  • Sequences
  • Spectra
  • Universities

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space