Distributed competition in dynamic networks

Consensus has been widely explored in the past years and successfully applied to the design of cooperative control laws and distributed computation paradigms. However, in the light of the great success of consensus in control, the counterpart of consensus, which, instead of mitigating the disagreement, increases the contrasts between dynamic agents in a distributed network, is still missing. The seminal work by Maass [1] (Maass, Neural Comput 12(11), 2519–2535, 2000) proves that weighted averaging, together with the operation of winner-take-all (WTA) organized in a two-layered structure is able to approximate any nonlinear mapping in any desired accuracy. When it comes to distributed networks, Maass’s theorem poses great appeal for distributed WTA algorithms provided that the distributed weighted averaging could be addressed using consensus. Unfortunately, as presented in Chaps. 1, 2, 3 and 4, there is no existing distributed WTA algorithm available, which significantly blocks the exhibition of the computational power of WTA over dynamic networks. In this chapter, we make progress along this direction and present the first distributed WTA protocol with guaranteed global convergence. The convergence to the WTA solution is proved rigorously using Lyapunov theory. The theoretical conclusions are supported by numerical validation.