Rendezvous Optimization for Second-Order Multiagent Systems: A Neurodynamic Approach With Generalized Compensation Term
针对二阶多智能体系统的会合优化问题，提出一种带广义补偿项的神经动力学方法，通过状态导数预测和约束补偿来抑制振荡，实现指数收敛到最优解。
This article investigates the rendezvous optimization problem for second-order multiagent systems. This task is typically framed as a convex optimization with equality constraints, which must also adhere to the system dynamics. Traditional neurodynamic approaches may lead to strong oscillations or instability due to uncoordinated intrinsic system dynamics. Inspired by proportional-derivative control and accelerated optimization techniques, a neurodynamic approach with a generalized compensation term (NGCT) is proposed to achieve oscillation suppression. The advantages of the approach include: 1) using state derivatives to provide predictions for oscillation suppression and 2) employing a compensation term based on the equality constraint coefficient matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$</tex-math> </inline-formula> to enhance constraint matching sensitivity. The transformation properties of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$</tex-math> </inline-formula> enable convergence to specified geometries. It is proven that the proposed approach exponentially converges to the optimal solution. Numerical experiments have demonstrated the effectiveness of the proposed approach in different rendezvous optimization problems.