Online Linear Quadratic Tracking With Regret Guarantees

Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online optimization where the time-varying reference state is unknown a pri...

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Published inIEEE control systems letters Vol. 7; p. 1
Main Authors Karapetyan, Aren, Bolliger, Diego, Tsiamis, Anastasios, Balta, Efe C., Lygeros, John
Format Journal Article
LanguageEnglish
Published IEEE 01.01.2023
Subjects
Complexity theory
Cost function
Costs
Heuristic algorithms
Online Control
Optimal Tracking
Steady-state
Target tracking
Trajectory
Online AccessGet full text
ISSN2475-1456
2475-1456
DOI10.1109/LCSYS.2023.3345809

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Abstract Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online optimization where the time-varying reference state is unknown a priori and is revealed after the applied control input. We show the equivalence of this problem to the control of linear systems subject to adversarial disturbances and propose a novel online gradient descent-based algorithm to achieve efficient tracking in finite time. We provide a dynamic regret upper bound scaling linearly with the path length of the reference trajectory and a numerical example to corroborate the theoretical guarantees.
AbstractList Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online optimization where the time-varying reference state is unknown a priori and is revealed after the applied control input. We show the equivalence of this problem to the control of linear systems subject to adversarial disturbances and propose a novel online gradient descent-based algorithm to achieve efficient tracking in finite time. We provide a dynamic regret upper bound scaling linearly with the path length of the reference trajectory and a numerical example to corroborate the theoretical guarantees.
Author Karapetyan, Aren
Balta, Efe C.
Tsiamis, Anastasios
Lygeros, John
Bolliger, Diego
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Snippet Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose...
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SubjectTerms Complexity theory
Cost function
Costs
Heuristic algorithms
Online Control
Optimal Tracking
Steady-state
Target tracking
Trajectory
Title Online Linear Quadratic Tracking With Regret Guarantees
URI https://ieeexplore.ieee.org/document/10368091
Volume 7
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