TY - JOUR

T1 - Online Convex Optimization for Data-Driven Control of Dynamical Systems

AU - Nonhoff, Marko

AU - Müller, Matthias A.

N1 - Publisher Copyright: © 2022 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.

PY - 2022/8/19

Y1 - 2022/8/19

N2 - We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown and time-varying cost functions. To this end, we make use of a single persistently exciting input-output sequence of the system and results from behavioral systems theory which enable it to handle unknown linear time-invariant systems. Moreover, we consider noisy output feedback instead of full state measurements and allow general economic cost functions. Our analysis of the closed loop reveals that the algorithm is able to achieve sublinear regret, where the measurement noise only adds an additional constant term to the regret upper bound. In order to do so, we derive a data-driven characterization of the steady-state manifold of an unknown system. Moreover, our algorithm is able to asymptotically exactly estimate the measurement noise. The effectiveness and applicational aspects of the proposed method are illustrated by means of a detailed simulation example in thermal control.

AB - We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown and time-varying cost functions. To this end, we make use of a single persistently exciting input-output sequence of the system and results from behavioral systems theory which enable it to handle unknown linear time-invariant systems. Moreover, we consider noisy output feedback instead of full state measurements and allow general economic cost functions. Our analysis of the closed loop reveals that the algorithm is able to achieve sublinear regret, where the measurement noise only adds an additional constant term to the regret upper bound. In order to do so, we derive a data-driven characterization of the steady-state manifold of an unknown system. Moreover, our algorithm is able to asymptotically exactly estimate the measurement noise. The effectiveness and applicational aspects of the proposed method are illustrated by means of a detailed simulation example in thermal control.

KW - Data-driven control

KW - linear systems

KW - online optimization

KW - optimal control

UR - http://www.scopus.com/inward/record.url?scp=85142876590&partnerID=8YFLogxK

U2 - 10.1109/OJCSYS.2022.3200021

DO - 10.1109/OJCSYS.2022.3200021

M3 - Article

VL - 1

SP - 180

EP - 193

JO - IEEE Open Journal of Control Systems

JF - IEEE Open Journal of Control Systems

SN - 2694-085X

ER -