Regularized Distributed MPC for UAV Networks: Stabilizing Coupled Motion and Hybrid Beam Alignment

Abstract

This letter investigates the coupled control problem in UAV networks utilizing high-frequency hybrid beamsteering. While phased arrays enable rapid electronic scanning, their finite Field of View (FoV) imposes a fundamental constraint that necessitates active mechanical steering of the airframe to maintain connectivity. We propose a decentralized Model Predictive Control (MPC) framework that jointly optimizes trajectory and heading to maximize network sum-capacity subject to safety constraints. Addressing the numerical instability caused by fast-fading channel nulls, we introduce a regularized surrogate cost function based on discrete spatial smoothing. We analytically prove that this approximation bounds the cost curvature, restoring the Lipschitz continuity of the gradient. Crucially, we derive a sufficient condition linking this Lipschitz constant to the controller gain, guaranteeing the contraction and linear convergence of the distributed best-response dynamics. Simulation results demonstrate that the proposed algorithm effectively navigates the trade-off between electronic beam tracking and kinematic safety, significantly systematically outperforming velocity-aligned baselines.