# On the Ergodic Control of Ensembles

arXiv: https://arxiv.org/abs/1807.03256 · HTML: https://mlsanity.com/paper/1807.03256/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 5 of 5)

- [Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants](https://mlsanity.com/paper/2110.03001/) (2021)
- [Subgroup Fairness in Two-Sided Markets](https://mlsanity.com/paper/2106.02702/) (2021)
- [Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions](https://mlsanity.com/paper/2209.01410/) (2022)
- [humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems](https://mlsanity.com/paper/2507.09626/) (2025)
- [Predictability and Fairness in Load Aggregation with Deadband](https://mlsanity.com/paper/2305.17725/) (2023)

## Abstract (arXiv)

Across smart-grid and smart-city application domains, there are many 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.