A $k$-Winners-Take-All $(k\text{WTA})$ Network with Noise Characteristics Captured

Competition-based $k-\mathbf{winners}-\mathbf{take}-\mathbf{all}\ \ (k \mathbf{WTA})$ networks play a crucial role in multi-agent systems. However, existing $k \mathbf{WTA}$ networks either neglect the impact of noise or only consider simple forms, such as constant noise. In practice, noises often exhibit time-varying and nonlinear characteristics, which can be modeled using nonlinear functions and approximated by high-order polynomials. Such noises pose significant challenges for current $k \mathbf{WTA}$ networks, limiting their practical applications. To address this, a $k \mathbf{WTA}$. network with noise characteristics captured $(k \mathbf{WTA}-\mathbf{NCC})$ is proposed in this article. Theoretical analyses demonstrate that the residual error of the proposed $k\mathbf{WTA}- \mathbf{NCC}$ network converges to zero globally, while simulation results confirm its robustness against polynomial noises. Additionally, a $k \mathbf{WTA}$ coordination model is constructed by integrating the proposed network with a consensus estimator to achieve multi-agent tracking tasks. Finally, simulations and physical experiments are conducted further to demonstrate the validity and practicality of the $k$ WTA coordination model.