Title: On the Ergodic Control of Ensembles,
Abstract: Across smart-grid and smart-city applications, there are problems where an
ensemble of agents is to be controlled such that both the aggregate behaviour
and individual-level perception of the system's performance are acceptable. In
many applications, traditional PI control is used to regulate aggregate
ensemble performance. Our principal contribution in this note is to demonstrate
that PI control may not be always suitable for this purpose, and in some
situations may lead to a loss of ergodicity for closed-loop systems. Building
on this observation, a theoretical framework is proposed to both analyse and
design control systems for the regulation of large scale ensembles of agents
with a probabilistic intent. Examples are given to illustrate our results.