On the ergodic control of ensembles

Abstract

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.

Distributed Ledger Technology for Smart Cities, the Sharing Economy, and Social Compliance

“…Another example of an important system of this type concerns irresponsible waste disposal. For example, in 2011 it was estimated that 2.5 billion coffee cups were thrown away (the figure is likely to be higher now) 8 . To many, decomposable cups are seen as the solution to this problem.…”

“…(iv) General compliance problems : It should be clear to the reader that there are many smart-city compliance problems where digital deposits can be used to enforce both human and machine behaviour. Examples include enforcing time-restricted parking, interfacing with 3D printers, gaining access to charge points, and ensuring that cyclists and car drivers comply with traffic light signalling (we shall see this 8 https://www.bbc.com/news/science-environment-43739043 last example in much more detail later). More generally, techniques to enforce compliance with social contracts are a fundamental part of any sharing economy system.…”

“…While items (i)-(iii) have attracted attention in the literature [5], [6], [7], [8], the very important issue of social compliance has been discussed to a much lesser degree, and it is in this context that we see DLT as a particularly attractive technology. Assuming that the reader is convinced of the merits of these applications, the reader may also ask why DLT is the method of choice for implementation.…”

Iterated Piecewise-Stationary Random Functions

“…Such extensions are important in applications where the number of agents may change over time (i.e., in almost all smart-city type applications, cf. [1,2,4]). Specifically, a criterion, implying uniqueness of piecewise-invariant measures in Polish space is developed in this note.…”

“…To this end, we need to model such an ensemble of agents. Some human-like behaviours and many complex decision-making strategies can be as modelled by iterated random functions [3,4]. In such systems, agents respond to a signal (for example, a price) or a system state with a probability that may depend on the state of the system (i.e., be "place-dependent").…”