We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is specified by L2/L1 or weighted L2/L1 norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed. Performance is measured by a modified LQ cost functional, penalising both the tracking error transient and the control effort. With such a cost functional, it is shown that a standard control design has divergent performance when the resolution of a `mono-resolution' approximator is increased. The class of `mono-resolution' approximators includes models popular in applications. A general construction of a class of approximators and their associated controllers which have a uniformly bounded performance independent of the resolution of the approximator is given.
%0 Journal Article
%1 french2000b
%A French, M.C.
%A Szepesvári, Cs.
%A Rogers, E.
%D 2000
%J Mathematics of Control, Signals and Systems
%K Lyapunov adaptive approximation, bounds, chain control, design, function integrators, multiresolution nonparametrics of performance theory, tracking,
%P 1--2
%T An Asymptotic Scaling Analysis of LQ performance for an Approximate Adaptive Control Design
%V 15
%X We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is specified by L2/L1 or weighted L2/L1 norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed. Performance is measured by a modified LQ cost functional, penalising both the tracking error transient and the control effort. With such a cost functional, it is shown that a standard control design has divergent performance when the resolution of a `mono-resolution' approximator is increased. The class of `mono-resolution' approximators includes models popular in applications. A general construction of a class of approximators and their associated controllers which have a uniformly bounded performance independent of the resolution of the approximator is given.
@article{french2000b,
abstract = {We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is specified by L2/L1 or weighted L2/L1 norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed. Performance is measured by a modified LQ cost functional, penalising both the tracking error transient and the control effort. With such a cost functional, it is shown that a standard control design has divergent performance when the resolution of a `mono-resolution' approximator is increased. The class of `mono-resolution' approximators includes models popular in applications. A general construction of a class of approximators and their associated controllers which have a uniformly bounded performance independent of the resolution of the approximator is given.},
added-at = {2020-03-17T03:03:01.000+0100},
author = {French, M.C. and Szepesv{\'a}ri, {Cs}. and Rogers, E.},
biburl = {https://www.bibsonomy.org/bibtex/2ccd08a32b3f5db5d19e1b0ea17faee5e/csaba},
date-added = {2010-08-28 17:38:14 -0600},
date-modified = {2010-09-05 01:18:16 -0600},
interhash = {eb1e87a948209f01ddc27c89b626c841},
intrahash = {ccd08a32b3f5db5d19e1b0ea17faee5e},
journal = {Mathematics of Control, Signals and Systems},
keywords = {Lyapunov adaptive approximation, bounds, chain control, design, function integrators, multiresolution nonparametrics of performance theory, tracking,},
pages = {1--2},
pdf = {http://eprints.ecs.soton.ac.uk/6643/1/csmcfetar_mcss2002.pdf},
timestamp = {2020-03-17T03:03:01.000+0100},
title = {An Asymptotic Scaling Analysis of {LQ} performance for an Approximate Adaptive Control Design},
volume = 15,
year = 2000
}