Network-decentralised optimisation and control

Network-decentralised optimisation and control: An explicit saturated solution

Blanchini, Franco (Università degli Studi di Udine)
Casagrande, Daniele (Università degli Studi di Udine)
Fabiani, F. (University of Pisa)
Giordano, G. (TU Delft Team Tamas Keviczky)
Pesenti, Raffaele (Università Ca’ Foscari Venezia)

2019

This paper proposes a decentralised explicit (closed-form) iterative formula that solves convex programming problems with linear equality constraints and interval bounds on the decision variables. In particular, we consider a team of decision agents, each setting the value of a subset of the variables, and a team of information agents, in charge of ensuring that the equality constraints are fulfilled. The structure of the constraint matrix imposes a communication pattern between decision and information agents, which can be represented as a bipartite graph. We associate each information agent with an integral variable and each decision agent with a saturated function, which takes the interval bounds into account, and we design a decentralised dynamic mechanism that globally converges to the optimal solution. Under mild conditions, the convergence is shown to be exponential. We also provide a discrete-time algorithm, based on the Euler system, and we give an upper bound for the step parameter to ensure convergence. Although the considered optimisation problem is static, we show that the proposed scheme can be successfully applied to find the optimal solution of network-decentralised dynamic control problems.

http://resolver.tudelft.nl/uuid:eab3b9b7-8f9c-4f41-81af-cce694220561

https://doi.org/10.1016/j.automatica.2019.02.009

2021-02-25

0005-1098

Automatica, 103, 379-389

Accepted Author Manuscript

Institutional Repository

journal article

© 2019 Franco Blanchini, Daniele Casagrande, F. Fabiani, G. Giordano, Raffaele Pesenti