Multilevel control by duality
Biccari U, Zuazua Iriondo E (2023)
Publication Language: English
Publication Status: Submitted
Publication Type: Journal article, Editorial
Future Publication Type: Journal article
Publication year: 2023
Journal
Book Volume: 175
Article Number: 105502
URI: https://arxiv.org/abs/2109.02346
DOI: 10.1016/j.sysconle.2023.105502
Open Access Link: https://arxiv.org/abs/2109.02346
Abstract
We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piecewise constant control function taking values in a finite set. In particular, we provide a complete characterization of multilevel controls through a duality approach, based on the minimization of a suitable cost functional. In this manner, we devise an effective methodology to systematically build optimal multilevel controls that, depending on the nature of the dynamics considered, have different structural properties. In more detail, in the case of conservative or dissipative dynamics, our technique allows us to define multilevel controls where the levels are fixed a priori, provided that the time horizon is large enough. For more general dynamics satisfying the Kalman rank condition, instead, we are able to build multilevel controls which are effective in any positive time T>0, whose levels blow-up as T→0+. Moreover, this method leads to efficient numerical algorithms for computing multilevel controls.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Spain (ES)How to cite
APA:
Biccari, U., & Zuazua Iriondo, E. (2023). Multilevel control by duality. Systems & Control Letters, 175. https://dx.doi.org/10.1016/j.sysconle.2023.105502
MLA:
Biccari, Umberto, and Enrique Zuazua Iriondo. "Multilevel control by duality." Systems & Control Letters 175 (2023).
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