A $k$WTA Network Based on Linear Programming Under Polynomial Noises With Applications
Mei Liu, Junsheng Ding, Xin Lv, Zhengtai Xie · IEEE Transactions on Industrial Electronics · 2025
Some existing$\boldsymbol{k}$-winners-take-all ($\boldsymbol{k}$WTA) networks are constructed based on the quadratic programming (QP), which have a high complexity in problem modeling. Others are designed based on linear programming (LP) but cannot effectively handle dynamic inputs and external interferences. This article employs the$\boldsymbol{k}$WTA problem based on the LP form, which offers a simpler framework for the network construction than those networks based on QP. Moreover, external interferences encountered during the implementation of the$\boldsymbol{k}$WTA operation are often characterized as complex noises which can be fitted by polynomials. To address these issues, a polynomial noise-tolerant$\boldsymbol{k}$WTA (PNT-$\boldsymbol{k}$WTA) network based on the LP is constructed that possesses the capability to suppress complex noises. Theoretical analyses establish the robustness and convergence of the proposed network, while numerical simulations demonstrate its superior performance compared to existing$\boldsymbol{k}$WTA networks. Finally, multi-robot target-tracking experiments confirm the PNT-$\boldsymbol{k}$WTA network’s practical effectiveness.