Gradient-Based Differential $k\text{WTA}$ Network With Application to Competitive Coordination of Multiple Robots

Aiming at the k-winners-take-all
$(k\text{WTA})$
operation, this paper proposes a gradient-based differential
$k\text{WTA}$
(GD-
$k\text{WTA}$
) network. After obtaining the network, theorems and related proofs are provided to guarantee the exponential convergence and noise resistance of the proposed GD-kWTA network. Then, numerical simulations are conducted to substantiate the preferable performance of the proposed network as compared with the traditional ones. Finally, the GD-kWTA network, backed with a consensus filter, is utilized as a robust control scheme for modeling the competition behavior in the multi-robot coordination, thereby further demonstrating its effectiveness and feasibility.