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:Proceedings of the American Control Conference pp. 2523 - 2528
Main Authors: Nonhoff, Marko, Muller, Matthias A.
Format: Conference Proceeding
Language:English
Published: American Automatic Control Council 25.05.2021
Subjects:
Control systems
Convex functions
Cost function
Heuristic algorithms
Prediction algorithms
Solids
Time measurement
ISSN:2378-5861
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 sub-linear regret is achieved if the variation of the cost functions is sublinear in time. Finally, we present an example to illustrate implementation details as well as the algorithm's performance and show that the proposed algorithm ensures constraint satisfaction.
ISSN:2378-5861
DOI:10.23919/ACC50511.2021.9482877