Tracking controllability for finite-dimensional linear systems

Zamorano Aliaga SA, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

Open Access Link: http://arxiv.org/abs/2407.18641

Abstract

We introduce and analyze the concept of tracking controllability, where the objective is for the state of a control system, or some projection thereof, to follow a given trajectory within a specified time horizon. By leveraging duality, we characterize tracking controllability through a non-standard observability inequality for the adjoint system. This characterization facilitates the development of a systematic approach for constructing controls with minimal norm. However, achieving such an observability property is challenging. To address this, we utilize the classical Brunovský canonical form for control systems, specifically focusing on the case of scalar controls. Our findings reveal that tracking control inherently involves a loss of regularity in the controls. This phenomenon is highly sensitive to the system's structure and the interaction between the projection to be tracked and the system.

Authors with CRIS profile

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

How to cite

APA:

Zamorano Aliaga, S.A., & Zuazua Iriondo, E. (2024). Tracking controllability for finite-dimensional linear systems. (Unpublished, Submitted).

MLA:

Zamorano Aliaga, Sebastian Andres, and Enrique Zuazua Iriondo. Tracking controllability for finite-dimensional linear systems. Unpublished, Submitted. 2024.

BibTeX: Download