Sparsity in control problems: Recent trends and open challenges
Abstract
As in all fields of engineering, control engineers constantly face a dichotomy between achieving high performance and the limited availability of resources for sensing, actuation, and control. This tension often translates into formalizing design problems with sparsity constraints; that is, the design involves decision variables whose number, spatial reach, temporal spread, or other physical expressions are much smaller than in the ideal scenario of unconstrained optimization of a task-related performance metric. Even though this fundamental limitation underlines a plethora of methodological approaches and application domains, the control literature is fragmented into several lines of work tailored to specific scenarios. This survey fills the gap by bringing together several lines of work on handling sparsity in relevant control problems such as actuator scheduling, minimal-energy controllability, maximum hands-off control, and online convex optimization, and weaving a red thread through theoretical foundations and algorithms. Beyond establishing a coherent, structured narrative of problems and solutions for handling sparsity in control scenarios, we discuss open areas and relevant directions for future research, motivated by the growing complexity of control systems and their relations with key domains such as pervasive computing, distributed learning, cyberphysical security, and ecological footprint.
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BibTeX
@misc{ballotta2026sparsity,
title = {{Sparsity in control problems: Recent trends and open challenges}},
author = {Luca Ballotta and Geethu Joseph and Waseem Abbas and Sophie M. Fosson and Chandra R. Murthy and Masaaki Nagahara and Alex Olshevsky and Kyle Poe and René Vidal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09787},
eprint = {2610.09787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09787},
}
RIS
TY - UNPB
TI - Sparsity in control problems: Recent trends and open challenges
AU - Luca Ballotta
AU - Geethu Joseph
AU - Waseem Abbas
AU - Sophie M. Fosson
AU - Chandra R. Murthy
AU - Masaaki Nagahara
AU - Alex Olshevsky
AU - Kyle Poe
AU - René Vidal
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.09787
UR - https://arxiv.org/abs/2610.09787
AB - As in all fields of engineering, control engineers constantly face a dichotomy between achieving high performance and the limited availability of resources for sensing, actuation, and control. This tension often translates into formalizing design problems with sparsity constraints; that is, the design involves decision variables whose number, spatial reach, temporal spread, or other physical expressions are much smaller than in the ideal scenario of unconstrained optimization of a task-related performance metric. Even though this fundamental limitation underlines a plethora of methodological approaches and application domains, the control literature is fragmented into several lines of work tailored to specific scenarios. This survey fills the gap by bringing together several lines of work on handling sparsity in relevant control problems such as actuator scheduling, minimal-energy controllability, maximum hands-off control, and online convex optimization, and weaving a red thread through theoretical foundations and algorithms. Beyond establishing a coherent, structured narrative of problems and solutions for handling sparsity in control scenarios, we discuss open areas and relevant directions for future research, motivated by the growing complexity of control systems and their relations with key domains such as pervasive computing, distributed learning, cyberphysical security, and ecological footprint.
ER -