@inproceedings{909138415f7e4e358387c714b8bd4e76,
title = "Geometry of adaptive control",
abstract = "Two incompatible topologies appear in the study of adaptive systems: The graph topology in control design, and the coefficient topology in system identification. Their incompatibility is manifest in the stabilization problem of adaptive control. We argue that this problem can be approached by changing the geometry of the sets of control systems under consideration: estimating n parameters in an n-dimensional manifold whose points all correspond to stabilizable systems. One way to accomplish this is using the properties of the algebraic Riccati equation. To illustrate the ideas we pose a simple parameter estimation problem as a constrained optimization problem, and show that it admits a unique minimum. Search algorithms in a hypersurface lead to adaptive controllers that combine ideas classified as direct and indirect adaptive control in the literature.",
keywords = "Adaptive control, Riccati equation, system identification, topology and geometry of control systems",
author = "Pait, {Felipe M.} and Benedetto Piccoli",
note = "Publisher Copyright: {\textcopyright} 2001 EUCA.; 6th European Control Conference, ECC 2001 ; Conference date: 04-09-2001 Through 07-09-2001",
year = "2001",
doi = "10.23919/ecc.2001.7076292",
language = "English (US)",
series = "2001 European Control Conference, ECC 2001",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "2439--2442",
booktitle = "2001 European Control Conference, ECC 2001",
address = "United States",
}