Fair and Sparse Solutions in Network-Decentralized Flow Control

Fair and Sparse Solutions in Network-Decentralized Flow Control

Blanchini, Franco (Università degli Studi di Udine)
Devia Pinzon, C.A. (TU Delft Team Tamas Keviczky)
Giordano, G. (Università di Trento)
Pesenti, Raffaele (Ca' Foscari University Venice)
Rosset, Francesca (Università degli Studi di Udine)

2022

We proposed network-decentralized control strategies, in which each actuator can exclusively rely on local information, without knowing the network topology and the external input, ensuring that the flow asymptotically converges to the optimal one with respect to the p -norm. For 1 < p < ∞ , the flow converges to a unique constant optimal up∗. We show that the state converges to the optimal Lagrange multiplier of the optimization problem. Then, we consider networks where the flows are affected by unknown spontaneous dynamics and the buffers need to be driven exactly to a desired set-point. We propose a network-decentralized proportional-integral controller that achieves this goal along with asymptotic flow optimality; now it is the integral variable that converges to the optimal Lagrange multiplier. The extreme cases p=1 and p=∞ are of some interest since the former encourages sparsity of the solution while the latter promotes fairness. Unfortunately, for p=1 or p=∞ these strategies become discontinuous and lead to chattering of the flow, hence no optimality is achieved. We then show how to approximately achieve the goal as the limit for p 1 or p ∞.

Actuators
buffer level control
Costs
Decentralized control
flow networks
Minimization
Optimization
p-norm minimisation
PI control
Steady-state
unknown dynamics

http://resolver.tudelft.nl/uuid:4ab6d99c-aab3-4f5b-bfe0-b0516f74a3c8

https://doi.org/10.1109/LCSYS.2022.3181341

2023-07-01

2475-1456

IEEE Control Systems Letters, 6, 2984-2989

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 Franco Blanchini, C.A. Devia Pinzon, G. Giordano, Raffaele Pesenti, Francesca Rosset