Social optimization problems with decentralized and selfish optimal strategies

Petros G. Voulgaris, Nicola Elia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider cooperative multi-agent systems minimizing a social cost. Each agent tries to minimize the deviation from the average collective behavior and to a local command input. In principle, the optimal solution is centralized and requires a complete communication graph. We study this problem for two important system input-output norms, the induced norm and the per-agent norm squared, as function of the number of agents, n. For the case of identical agents, we show that the optimal social solution is always decentralized and characterize the local optimization problem each agent needs to solve. The solution is decentralized but not selfish in the sense that the local optimization problem is not the same as that of a single isolated agent and also depends on the number of agents. In the case of the per-agent H2 norm squared cost, we have similar results. However, in this case, we show that the optimal decentralized selfish solution is socially optimal in the limit of large n. We study some extensions that include norm constraints, and performance indices not restricted to only penalizing the variations for averages. We also present some extensions of the results to the cases of nonuniform averaging and non uniform agent dynamics. In simple terms, these results, identify important problem classes where decentralized and possibly selfish behaviors are socially optimal, and for which inter-agent communication is unnecessary.

Original languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4721-4726
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Other

Other56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

ASJC Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

Fingerprint Dive into the research topics of 'Social optimization problems with decentralized and selfish optimal strategies'. Together they form a unique fingerprint.

  • Cite this

    Voulgaris, P. G., & Elia, N. (2018). Social optimization problems with decentralized and selfish optimal strategies. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 4721-4726). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264357