Details
| Original language | English |
|---|---|
| Article number | 105532 |
| Journal | Systems and Control Letters |
| Volume | 177 |
| Early online date | 7 May 2023 |
| Publication status | Published - Jul 2023 |
Abstract
In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret implies asymptotic stability of the optimal steady state for a constant cost function. For the case of an asymptotically stable closed loop, we first derive a necessary condition for achieving bounded dynamic regret. Then, given some additional assumptions on the system and the cost functions, we also provide a sufficient condition ensuring bounded dynamic regret. Our results are illustrated by examples.
Keywords
- Asymptotic stability, Dynamic regret, Online convex optimization, Time-varying optimal control
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- General Computer Science
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Electrical and Electronic Engineering
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In: Systems and Control Letters, Vol. 177, 105532, 07.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the relation between dynamic regret and closed-loop stability
AU - Nonhoff, Marko
AU - Müller, Matthias A.
N1 - Funding Information: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 505182457 .
PY - 2023/7
Y1 - 2023/7
N2 - In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret implies asymptotic stability of the optimal steady state for a constant cost function. For the case of an asymptotically stable closed loop, we first derive a necessary condition for achieving bounded dynamic regret. Then, given some additional assumptions on the system and the cost functions, we also provide a sufficient condition ensuring bounded dynamic regret. Our results are illustrated by examples.
AB - In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret implies asymptotic stability of the optimal steady state for a constant cost function. For the case of an asymptotically stable closed loop, we first derive a necessary condition for achieving bounded dynamic regret. Then, given some additional assumptions on the system and the cost functions, we also provide a sufficient condition ensuring bounded dynamic regret. Our results are illustrated by examples.
KW - Asymptotic stability
KW - Dynamic regret
KW - Online convex optimization
KW - Time-varying optimal control
UR - http://www.scopus.com/inward/record.url?scp=85158027121&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2209.05964
DO - 10.48550/arXiv.2209.05964
M3 - Article
AN - SCOPUS:85158027121
VL - 177
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
M1 - 105532
ER -