Finite-Time Convergent and Weight-Unbalanced $k$WTA Network With Multirobot Competitive Coordination

A weight-unbalanced
$k$
-winner-take-all (WU-
$k$
WTA) network with finite-time convergence is constructed, analyzed, and applied to undirected and directed multirobot systems with unbalanced weights of communication topology. The convergent time of the finite-time
$k$
WTA network is theoretically derived with theorems proof. Furthermore, comparisons are conducted among the proposed WU-
$k$
WTA network and other existing
$k$
WTA works, and results reveal that the proposed network has high precision when encountering undirected or directed weight-unbalanced topologies. Additionally, a dynamic target tracking algorithm is established by employing the proposed WU-
$k$
WTA network, and its feasibility and efficiency are validated via simulations on a multirobot system and an experiment on the E-puck robot physical platform.