Classical d-Step-Ahead Adaptive Control Revisited: Linear-Like Convolution Bounds and Exponential Stability (Extended Version)
Abstract
Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In recent work it has been shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, Projection Algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed loop behaviour can be proven; this immediately confers exponential stability and a bounded noise gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper we extend the approach to the d-step-ahead adaptive controller setting and prove comparable properties.
Cite
@article{arxiv.1902.09372,
title = {Classical d-Step-Ahead Adaptive Control Revisited: Linear-Like Convolution Bounds and Exponential Stability (Extended Version)},
author = {Daniel E Miller and Mohamad T. Shahab},
journal= {arXiv preprint arXiv:1902.09372},
year = {2019}
}
Comments
This is an extended version of a paper which will appear at the 2019 American Control Conference. arXiv admin note: text overlap with arXiv:1705.01494