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 proportional-integral (PI) control is used to regulate aggregate ensemble performance. We 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.
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