Discrete observability and numerical quadrature

Author

Martin, Clyde F. ; Wang, Xiaochang ; Stamp, Mark

Author_Institution

Dept. of Math., Texas Tech. Univ., Lubbock, TX, USA

Volume

36

Issue

11

fYear

1991

fDate

11/1/1991 12:00:00 AM

Firstpage

1337

Lastpage

1340

Abstract

The author consider the problem of approximate observability of a one-dimensional diffusion equation on a finite spatial domain with spatial point measurements. The problem of the optimal selection of the measurement points is considered under three conditions: (1) no preassigned measurement nodes; (2) one preassigned node and; (3) two preassigned nodes. The main observation is that the optimal choice is related to three classical procedures in numerical analysis: (1) Gaussian quadrature; (2) Radau quadrature and; (3) Lobatto quadrature. It is shown that the existence of the Radau and Lobatto quadrature is closely related to classical root locus theory

Keywords

diffusion; observability; optimisation; 1D diffusion equation; Gaussian quadrature; Lobatto quadrature; Radau quadrature; discrete observability; numerical quadrature; preassigned node; root locus theory; Boundary conditions; Eigenvalues and eigenfunctions; Equations; Force measurement; Mathematics; NASA; Numerical analysis; Observability; Polynomials; Sampling methods;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.100950

Filename

100950