Model-Free Learning for Massive MIMO Systems: Stochastic Approximation Adjoint Iterative Learning Control

Leontine Aarnoudse (Corresponding author), Tom Oomen

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2 Citations (Scopus)
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Learning can substantially increase the performance of control systems that perform repeating tasks. The aim of this letter is to develop an efficient iterative learning control algorithm for MIMO systems with a large number of inputs and outputs that does not require model knowledge. The gradient of the control criterion is obtained through dedicated experiments on the system. Using a judiciously selected randomization technique, an unbiased estimate of the gradient is obtained from a single dedicated experiment, resulting in fast convergence of a Robbins-Monro type stochastic gradient descent algorithm. Analysis shows that the approach is superior to earlier deterministic approaches and to related SPSA-Type algorithms. The approach is illustrated on a multivariable example.

Original languageEnglish
Article number9300146
Pages (from-to)1946-1951
Number of pages6
JournalIEEE Control Systems Letters
Issue number6
Publication statusPublished - Dec 2021

Bibliographical note

Funding Information:
Manuscript received September 11, 2020; revised November 23, 2020; accepted December 12, 2020. Date of publication December 21, 2020; date of current version March 8, 2021. This work was supported by the Netherlands Organization for Scientific Research (NWO) through Research Programme VIDI under Project 15698. Recommended by Senior Editor G. Cherubini. (Corresponding author: Leontine Aarnoudse.) The authors are with the Department of Mechanical Engineering, Control Systems Technology, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands (e-mail:; Digital Object Identifier 10.1109/LCSYS.2020.3046169


  • Iterative learning control
  • large-scale systems
  • optimization
  • randomized algorithms


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