Controllability Canonical Forms of Linear Ensemble Systems Article Swipe
Wei Zhang
,
Jr-Shin Li
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2211.02975
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2211.02975
Ensemble control, an emerging research field focusing on the study of large populations of dynamical systems, has demonstrated great potential in numerous scientific and practical applications. Striking examples include pulse design for exciting spin ensembles in quantum physics, neurostimulation for relieving neurological disorder symptoms, and path planning for steering robot swarms. However, the control targets in such applications are generally large-scale complex and severely underactuated ensemble systems, research into which stretches the capability of techniques in classical control and dynamical systems theory to the very limit. This paper then devotes to advancing our knowledge about controllability of linear ensemble systems by integrating tools in modern algebra into the technique of separating points developed in our recent work. In particular, we give an algebraic interpretation of the dynamics of linear systems in terms of actions of polynomials on vector spaces, and this leads to the development of the functional canonical form of matrix-valued functions, which can also be viewed as the generalization of the rational canonical form of matrices in linear algebra. Then, leveraging the technique of separating points, we achieve a necessary and sufficient characterization of uniform ensemble controllability for time-invariant linear ensemble systems as the ensemble controllability canonical form, in which the system and control matrices are in the functional canonical and block diagonal form, respectively. This work successfully launches a new research scheme by adopting and tailoring finite-dimensional methods to tackle control problems involving infinite-dimensional ensemble systems, and lays a solid foundation for a more inclusive ensemble control theory targeting a much broader spectrum of control and learning problems in both scientific research and practice.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2211.02975
- https://arxiv.org/pdf/2211.02975
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4308612050
All OpenAlex metadata
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https://openalex.org/W4308612050Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2211.02975Digital Object Identifier
- Title
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Controllability Canonical Forms of Linear Ensemble SystemsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-11-05Full publication date if available
- Authors
-
Wei Zhang, Jr-Shin LiList of authors in order
- Landing page
-
https://arxiv.org/abs/2211.02975Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2211.02975Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2211.02975Direct OA link when available
- Concepts
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Controllability, Dynamical systems theory, Canonical form, Linear dynamical system, Linear algebra, Linear system, Canonical ensemble, Computer science, Mathematics, Pure mathematics, Applied mathematics, Physics, Quantum mechanics, Statistics, Mathematical analysis, Monte Carlo method, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.dynamical | 14, 79 |
| abstract_inverted_index.ensembles | 34 |
| abstract_inverted_index.generally | 59 |
| abstract_inverted_index.inclusive | 247 |
| abstract_inverted_index.involving | 235 |
| abstract_inverted_index.knowledge | 93 |
| abstract_inverted_index.necessary | 181 |
| abstract_inverted_index.potential | 19 |
| abstract_inverted_index.practical | 24 |
| abstract_inverted_index.practice. | 266 |
| abstract_inverted_index.relieving | 40 |
| abstract_inverted_index.stretches | 70 |
| abstract_inverted_index.symptoms, | 43 |
| abstract_inverted_index.tailoring | 228 |
| abstract_inverted_index.targeting | 251 |
| abstract_inverted_index.technique | 108, 174 |
| abstract_inverted_index.capability | 72 |
| abstract_inverted_index.foundation | 243 |
| abstract_inverted_index.functional | 147, 210 |
| abstract_inverted_index.functions, | 152 |
| abstract_inverted_index.leveraging | 172 |
| abstract_inverted_index.scientific | 22, 263 |
| abstract_inverted_index.separating | 110, 176 |
| abstract_inverted_index.sufficient | 183 |
| abstract_inverted_index.techniques | 74 |
| abstract_inverted_index.development | 144 |
| abstract_inverted_index.integrating | 101 |
| abstract_inverted_index.large-scale | 60 |
| abstract_inverted_index.particular, | 118 |
| abstract_inverted_index.polynomials | 135 |
| abstract_inverted_index.populations | 12 |
| abstract_inverted_index.applications | 57 |
| abstract_inverted_index.demonstrated | 17 |
| abstract_inverted_index.neurological | 41 |
| abstract_inverted_index.successfully | 219 |
| abstract_inverted_index.applications. | 25 |
| abstract_inverted_index.matrix-valued | 151 |
| abstract_inverted_index.respectively. | 216 |
| abstract_inverted_index.underactuated | 64 |
| abstract_inverted_index.generalization | 160 |
| abstract_inverted_index.interpretation | 123 |
| abstract_inverted_index.time-invariant | 190 |
| abstract_inverted_index.controllability | 95, 188, 197 |
| abstract_inverted_index.characterization | 184 |
| abstract_inverted_index.neurostimulation | 38 |
| abstract_inverted_index.finite-dimensional | 229 |
| abstract_inverted_index.infinite-dimensional | 236 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/11 |
| sustainable_development_goals[0].score | 0.5199999809265137 |
| sustainable_development_goals[0].display_name | Sustainable cities and communities |
| citation_normalized_percentile |