An asymptotic scaling analysis of LQ performance of an approximate adaptive control design

French, M., Szepesvari, Cs. and Rogers, E. (2002) An asymptotic scaling analysis of LQ performance of an approximate adaptive control design. Mathematics of Control, Signals and Systems, 15, 145-176.

Record type: Article

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/L^∞ or weighted L²/L^∞ norm bounds. We analyse a standard Lyapunov-based adaptive design which utilises 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 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.

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