A redesign methodology generating predefined‐time differentiators with bounded time‐varying gains Article Swipe
Rodrigo Aldana‐López
,
Richard Seeber
,
David Gómez‐Gutiérrez
,
Marco Tulio Angulo
,
Michaël Defoort
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1002/rnc.6315
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1002/rnc.6315
There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, that is, which are fixed‐time convergent with a predefined upper bound of their settling time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their th time derivative, the existing design methodologies yield a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time‐varying gains (TVG) to design arbitrary‐order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded TVG. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how TVG offer a general and flexible methodology to design algorithms with a predefined UBST.
Related Topics
Concepts
Differentiator
Bounded function
Settling time
A priori and a posteriori
Upper and lower bounds
Convergence (economics)
Mathematical optimization
Control theory (sociology)
Computer science
Set (abstract data type)
Mathematics
Dwell time
Filter (signal processing)
Applied mathematics
Control (management)
Step response
Programming language
Clinical psychology
Mathematical analysis
Medicine
Engineering
Control engineering
Artificial intelligence
Economics
Computer vision
Economic growth
Philosophy
Epistemology
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1002/rnc.6315
- OA Status
- green
- Cited By
- 33
- References
- 54
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4286381971
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4286381971Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1002/rnc.6315Digital Object Identifier
- Title
-
A redesign methodology generating predefined‐time differentiators with bounded time‐varying gainsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-08-03Full publication date if available
- Authors
-
Rodrigo Aldana‐López, Richard Seeber, David Gómez‐Gutiérrez, Marco Tulio Angulo, Michaël DefoortList of authors in order
- Landing page
-
https://doi.org/10.1002/rnc.6315Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2106.06429Direct OA link when available
- Concepts
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Differentiator, Bounded function, Settling time, A priori and a posteriori, Upper and lower bounds, Convergence (economics), Mathematical optimization, Control theory (sociology), Computer science, Set (abstract data type), Mathematics, Dwell time, Filter (signal processing), Applied mathematics, Control (management), Step response, Programming language, Clinical psychology, Mathematical analysis, Medicine, Engineering, Control engineering, Artificial intelligence, Economics, Computer vision, Economic growth, Philosophy, EpistemologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
33Total citation count in OpenAlex
- Citations by year (recent)
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2025: 6, 2024: 10, 2023: 15, 2022: 2Per-year citation counts (last 5 years)
- References (count)
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54Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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