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

摘要

Aiming at the k-winners-take-all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k\text{WTA})$</tex> operation, this paper proposes a gradient-based differential <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k\text{WTA}$</tex> (GD- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k\text{WTA}$</tex> ) 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.