We revisit the recent gradient tracking algorithm for distributed consensus optimization from a control theoretic viewpoint. We show that the algorithm can be constructed by solving a servomechanism control problem stemming from the distributed implementation of a centralized gradient method. Moreover, we show that, if expressed in proper coordinates, the gradient tracking embeds an integral action fed by a signal related to the consensus error. Finally, we provide an alternative convergence analysis based on Lyapunov arguments that also proves exponential asymptotic stability of the optimal equilibrium.

Notarnicola, I., Bin, M., Marconi, L., Notarstefano, G. (2023). The Gradient Tracking Is a Distributed Integral Action. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 68(12), 7911-7918 [10.1109/tac.2023.3248487].

The Gradient Tracking Is a Distributed Integral Action

Notarnicola, Ivano
Primo
;
Bin, Michelangelo
Secondo
;
Marconi, Lorenzo
Penultimo
;
Notarstefano, Giuseppe
Ultimo
2023

Abstract

We revisit the recent gradient tracking algorithm for distributed consensus optimization from a control theoretic viewpoint. We show that the algorithm can be constructed by solving a servomechanism control problem stemming from the distributed implementation of a centralized gradient method. Moreover, we show that, if expressed in proper coordinates, the gradient tracking embeds an integral action fed by a signal related to the consensus error. Finally, we provide an alternative convergence analysis based on Lyapunov arguments that also proves exponential asymptotic stability of the optimal equilibrium.
2023
Notarnicola, I., Bin, M., Marconi, L., Notarstefano, G. (2023). The Gradient Tracking Is a Distributed Integral Action. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 68(12), 7911-7918 [10.1109/tac.2023.3248487].
Notarnicola, Ivano; Bin, Michelangelo; Marconi, Lorenzo; Notarstefano, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/959315
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