Integral Quadratic Constraints with Infinite-Dimensional Channels Article Swipe
Aleksandr Talitckii
,
Matthew M. Peet
,
Peter Seiler
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.23919/acc55779.2023.10156335
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.23919/acc55779.2023.10156335
Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinite-dimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinite-dimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity.
Related Topics
Concepts
Mathematics
Quadratic equation
Nonlinear system
Partial differential equation
Lemma (botany)
Control theory (sociology)
Interconnection
Applied mathematics
Stability (learning theory)
Mathematical analysis
Computer science
Physics
Ecology
Biology
Poaceae
Quantum mechanics
Computer network
Artificial intelligence
Machine learning
Control (management)
Geometry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.23919/acc55779.2023.10156335
- OA Status
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- References
- 27
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4382935678Canonical identifier for this work in OpenAlex
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https://doi.org/10.23919/acc55779.2023.10156335Digital Object Identifier
- Title
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Integral Quadratic Constraints with Infinite-Dimensional ChannelsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
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2023-05-31Full publication date if available
- Authors
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Aleksandr Talitckii, Matthew M. Peet, Peter SeilerList of authors in order
- Landing page
-
https://doi.org/10.23919/acc55779.2023.10156335Publisher landing page
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://pmc.ncbi.nlm.nih.gov/articles/PMC10387136/pdf/nihms-1917830.pdfDirect OA link when available
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Mathematics, Quadratic equation, Nonlinear system, Partial differential equation, Lemma (botany), Control theory (sociology), Interconnection, Applied mathematics, Stability (learning theory), Mathematical analysis, Computer science, Physics, Ecology, Biology, Poaceae, Quantum mechanics, Computer network, Artificial intelligence, Machine learning, Control (management), GeometryTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| referenced_works_count | 27 |
| abstract_inverted_index.a | 6, 46, 118, 143, 159 |
| abstract_inverted_index.In | 83 |
| abstract_inverted_index.We | 130 |
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| abstract_inverted_index.which | 41 |
| abstract_inverted_index.(KYP). | 166 |
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| abstract_inverted_index.extend | 78 |
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| abstract_inverted_index.widely | 65 |
| abstract_inverted_index.(DDEs). | 100 |
| abstract_inverted_index.(IQCs), | 40 |
| abstract_inverted_index.(ODEs), | 71 |
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| abstract_inverted_index.Perhaps | 24 |
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| abstract_inverted_index.Equations | 70, 94, 99 |
| abstract_inverted_index.IQC-based | 89, 122 |
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| abstract_inverted_index.illustrated | 171 |
| abstract_inverted_index.multipliers | 141 |
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| abstract_inverted_index.multipliers. | 129 |
| abstract_inverted_index.nonlinearity. | 179 |
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| abstract_inverted_index.interconnections. | 110 |
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| abstract_inverted_index.Kalman-Yakubovich-Popov | 164 |
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| citation_normalized_percentile.is_in_top_10_percent | False |