An online convex optimization algorithm for controlling linear systems with state and input constraints

This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost functions while restraining the system states and inputs to poly...

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Veröffentlicht in:arXiv.org
Hauptverfasser: Nonhoff, Marko, Müller, Matthias A
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 16.03.2021
Schlagworte:
Algorithms
Computational geometry
Convexity
Cost function
Linear systems
Optimization
ISSN:2331-8422
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Abstract This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost functions while restraining the system states and inputs to polytopic constraint sets. Analysis of the algorithm's performance, measured by dynamic regret, reveals that sublinear regret is achieved if the variation of the cost functions is sublinear in time. Finally, we present a simple example to illustrate implementation details as well as the algorithm's performance and show that the proposed algorithm ensures constraint satisfaction.
AbstractList This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost functions while restraining the system states and inputs to polytopic constraint sets. Analysis of the algorithm's performance, measured by dynamic regret, reveals that sublinear regret is achieved if the variation of the cost functions is sublinear in time. Finally, we present a simple example to illustrate implementation details as well as the algorithm's performance and show that the proposed algorithm ensures constraint satisfaction.
Author Nonhoff, Marko
Müller, Matthias A
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Computational geometry
Convexity
Cost function
Linear systems
Optimization
Title An online convex optimization algorithm for controlling linear systems with state and input constraints
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