%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 }