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

Richard E. Groff, University of Michigan
Pramod P. Khargonekar, University of Florida
Daniel E. Koditschek, University of Pennsylvania

Article 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.

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.