Linear Smoothing of Singularly Perturbed Systems.

Abstract

A near optimal fixed-interval smoother for singularly perturbed systems is derived using the two filter (forward and backward) formulation. This intuitively-pleasing approach simplifies the fast mode boundary layer complications encountered previously, and results in a much simpler implementation than the exact solution. Application of similar singular perturbation techniques as for the (forward) filters, to the backward filter, results in a near optimal smoother with a similar two time-scale solution for the fast and slow modes. The alternative use of the unrealizable Wiener filter for the fast mode is justified in the interior of the smoothing interval. Finally, a numerical example serves to illustrate how well the near optimal design approximates the exact for various values of the perturbation parameter mu.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA038268

Entities

People

  • Dean Altshuler

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Boundaries
  • Boundary Layer
  • Computational Complexity
  • Equations
  • Equations Of State
  • Estimators
  • Filters
  • Filtration
  • Illinois
  • Intervals
  • Layers
  • New York
  • Riccati Equation
  • Steady State
  • United States
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Plasma Physics / Magnetohydrodynamics