A Local Convergence Proof for the Minvar Algorithm for Computing Continuous Piecewise Linear Approximations

Loading...
Thumbnail Image
Penn collection
Departmental Papers (ESE)
General Robotics, Automation, Sensing and Perception Laboratory
Kod*lab
Degree type
Discipline
Subject
GRASP
Kodlab
piecewise linear
invertible approximation
moving mesh
triangulation
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Groff, Richard E
Khargonekar, Pramod P
Contributor
Abstract

The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction of a forward and inverse system model from data. Most approximation techniques require that separate forward and inverse models be trained, whereas an invertible continuous PL affords, simultaneously, the forward and inverse system model in a single representation. The minvar algorithm computes a continuous PL approximation to data. Local convergence of minvar is proven for the case when the data generating function is itself a PL function and available directly rather than through data.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2003-03-01
Journal title
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Reprinted from SIAM Journal on Numerical Analysis, Volume 41, Issue 3, 2003, pages 87-93. Publisher URL: http://dx.doi.org/10.1137/S0036142902402213 NOTE: At the time of publication the author, Daniel Koditschek, was affiliated with the University of Michigan. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania.
Recommended citation
Collection