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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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Nonhoff, Marko, Müller, Matthias A
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 16.03.2021
Subjects:	Algorithms Computational geometry Convexity Cost function Linear systems Optimization
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2005.11308