Estimation for Boundary-Value Descriptor Systems

Abstract

In this paper we consider models for noncausal processes consisting of discrete-time descriptor dynamics and boundary conditions on the values of the process at the two ends of the interval on which the process is defined. We discuss the general solution and well-posedness of systems of this type and then apply the method of complementary processes to obtain a specification of the optimal smoother in terms of a boundary-value descriptor Hamiltonian system. We then study the implementation of the optimal smoother. Motivated by the Hamiltonian diagonalization results for non-descriptor systems we show how the descriptor Hamiltonian dynamics can be transformed to two lower-order systems by the use of transformation matrices involving the solution of two generalized Riccati equations. We present several examples illustrating our results and the nature of the smoothing solution and also present equations for covariance analysis of boundary-value descriptor processes including the smoothing error.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1988
Accession Number
ADA458132

Entities

People

  • Alan S. Willsky
  • Bernard C. Lévy
  • Milton B. Adams
  • Ramine Nikoukhah

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Computations
  • Computer Science
  • Covariance
  • Difference Equations
  • Dynamics
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Equations
  • Random Variables
  • Riccati Equation
  • Sequences
  • Standards
  • Stochastic Processes
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis