Consensus algorithms are routinely employed in a variety of multi-agent scenarios. They require that each agent iteratively evaluates a multivariate function of its neighbours’ information states. If a wireless communication channel is used, this is typically implemented through protocols (such as TDMA – Time Division Multiple Access) that avoid superposition of transmitted signals by assigning each transmitter its own (time) slot.
However, consensus only requires that agents know a function of their neighbours’ information states, not the individual information states. Hence one may ask whether using the famous Kolmogorov-Arnold representation theorem might allow to exploit the channel’s superposition property to drastically reduce communication effort. Kolmogorov-Arnold essentially states that every continuous multivariate function can be expressed via univariate functions and addition. If channel superposition were to be considered as addition, all agents could consequently simultaneously transmit a suitably preprocessed version of their information state, with receiving agents locally postprocessing the received superposition signal.

We will explain for two widely used consensus types (average consensus and max-consensus) why in practice the application of Kolmogorov-Arnold is not
quite as straightforward. For both consensus types, we will suggest alternative approaches, which make use of the channel’s superposition property while
handling non-ideality effects such as time-varying unknown channel coefficients. By allowing all agents to transmit at the same time, the required number of
transmission slots is considerably reduced. In the second part of the talk, we will demonstrate how average and max-consensus algorithms can be used in various traffic automation scenarios. This includes platooning, distributed automatic lane changing, and distributed automation of traffic intersections.