Optimal actuator design via Brunovsky’s normal form

Geshkovski B, Zuazua Iriondo E (2022)

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2022

Journal

IEEE Transactions on Automatic Control

Publisher: IEEE Automatic Control

Book Volume: 26

Journal Issue: 12

URI: https://dcn.nat.fau.eu/wp-content/uploads/2108.05629.pdf

DOI: 10.1109/TAC.2022.3181222

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/2108.05629.pdf

Abstract

In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such systems may be seen as spatially discretized linear partial differential equations with lumped controls. The change of coordinates induced by Brunovsky’s normal form allows us to remove the restriction of having to work with diagonalizable system dynamics, and does not entail a randomization procedure as done in past literature on diffusion equations or waves. Instead, the optimization problem reduces to a minimization of the norm of the inverse of a change of basis matrix, and allows for an easy deduction of existence of solutions, and for a clearer picture of some of the problem’s intrinsic symmetries. Numerical experiments help to visualize these artifacts, indicate further open problems, and also show a possible obstruction of using gradient-based algorithms – this is alleviated by using an evolutionary algorithm.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Massachusetts Institute of Technology (MIT) US United States (USA) (US)

How to cite

APA:

Geshkovski, B., & Zuazua Iriondo, E. (2022). Optimal actuator design via Brunovsky’s normal form. IEEE Transactions on Automatic Control, 26(12). https://doi.org/10.1109/TAC.2022.3181222

MLA:

Geshkovski, Borjan, and Enrique Zuazua Iriondo. "Optimal actuator design via Brunovsky’s normal form." IEEE Transactions on Automatic Control 26.12 (2022).

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