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.

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How to cite

APA:

Biccari, U., & Zuazua Iriondo, E. (2023). Multilevel control by duality. Systems & Control Letters, 175. https://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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