In this paper, we take an input-output approach to enhance the study of cooperative multiagent optimization problems that admit decentralized and selfish solutions, hence eliminating the need for an interagent communication network. The framework under investigation is a set of n independent agents coupled only through an overall cost that penalizes the divergence of each agent from the average collective behavior. In the case of identical agents, or more generally agents with identical essential input-output dynamics, we show that optimal decentralized and selfish solutions are possible in a variety of standard input-output cost criteria. These include the cases of ℓ1, ℓ2, ℓ∞ induced, and H2 norms for any finite n. Moreover, if the cost includes non-deviation from average variables, the above results hold true as well for ℓ1, ℓ2, ℓ∞ induced norms and any n, while they hold true for the normalized, per-agent square H2 norm, cost as n→∞. We also consider the case of nonidentical agent dynamics and prove that similar results hold asymptotically as n→∞ in the case of ℓ2 induced norms (i.e., H∞) under a growth assumption on the H∞ norm of the essential dynamics of the collective.
|Original language||English (US)|
|Title of host publication||2018 Annual American Control Conference, ACC 2018|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - Aug 9 2018|
|Event||2018 Annual American Control Conference, ACC 2018 - Milwauke, United States|
Duration: Jun 27 2018 → Jun 29 2018
|Name||Proceedings of the American Control Conference|
|Other||2018 Annual American Control Conference, ACC 2018|
|Period||6/27/18 → 6/29/18|
Bibliographical noteFunding Information:
This work was supported in part by the National Science Foundation under NSF Awards CMMI-1663460, ECCS-1739732, NSF ECCS 10-27437 and CCF 1320643, and AFOSR under Awards AF FA 9550-12-1-0193 and FA 9550-15-1-0119.
© 2018 AACC.