Design, analysis, and application of projected k-winner-take-all network

Competition is considered to be a driving force of many swarm systems in maintaining vitality, as important as collaboration. To model this competitive nature, an operation called -winner-take-all (WTA) is introduced that can output maximum values from input signals with . In this paper, different projection functions (PFs) are combined with WTA operations as activation functions for the first time, and a P-WTA network is proposed, analyzed, and applied, which accelerates the convergence rate and enhances the robustness of existing models. With the aid of various characteristics, such as saturated or nonconvex, the convergent process of the proposed P-WTA network is able to present diverse effects of PFs. Additionally, numerical simulations, an application to a multi-agent system, and an experiment of multiple E-puck robots on the CoppeliaSim platform all demonstrate the feasibility and effectiveness of the P-WTA network.