Results in cooperative control and implicit consensus

Abstract

This paper is concerned with a class of decentralised control problems that arise in contemporary applications where agents cooperate to control and regulate a global quantity, are limited in the manner in which they communicate with each other, and are required to reach consensus on some implicit variable (for example, CO 2 emissions). Three algorithms are presented for achieving this goal. The convergence of these algorithms are proven, and their efficacy is demonstrated in simulations.

A result on implicit consensus with application to emissions control

“…Conversely, the utility functions may not be of static but dynamical nature. In this case, the utility values may be filtered values of the physical state, a set-up that is also considered in [3]. Due to space limitations, we cannot discuss these results here.…”

“…These conditions guarantee that the continuous utility functions are strictly monotone increasing and unbounded and thus have continuous inverse functions φ (i) so that φ (i) f (i) (r) = r and f (i) φ (i) (t) = t for all t, r ∈ R. Given these conditions, it can easily be shown that the problem always has a unique feasible solution, [3].…”

“…The algorithm can easily be extended to cases where not all nodes have access to the global value (it can be shown that it is sufficient for only one node to have access to this value) as well cases of asynchronous communications and state updates, see [3] for more details.…”

“…The main contributions of this paper is a theorem coupled with an application which consists of a cooperative control scheme designed for city-wide CO 2 emissions control with Plug-in Hybrid Electric Vehicles (PHEVs). It is based on results of a recently accepted paper [3], which we reproduce here in a condensed form.…”

Cooperative Regulation and Trading of Emissions Using Plug-in Hybrid Vehicles

“…Amazingly, just how damaging to health those vehicles can be, appears not to be widely appreciated by the general public with public discourse focussing mainly on greenhouse emissions and on vehicle safety. This basic fact provides the main motivation for this and prior work [13,14]; namely, to investigate methods based on V2X to contribute to the regulation of air quality in our cities.…”