Toward Dual-Functional LAWN: Control-Aware System Design for Aerodynamics-Aided UAV Formations

Integrated sensing and communication (ISAC) has emerged as a pivotal technology for advancing low-altitude wireless networks (LAWNs), serving as a critical enabler for next-generation communication systems. This paper investigates the system design for energy-saving unmanned aerial vehicle (UAV) formations in dual-functional LAWNs, where a ground base station (GBS) simultaneously wirelessly controls multiple UAV formations and performs sensing tasks. To enhance flight endurance, we exploit the aerodynamic upwash effects and propose a distributed energy-saving formation framework based on the adapt-then-combine (ATC) diffusion least mean square (LMS) algorithm. Specifically, each UAV updates the local position estimate by invoking the LMS algorithm, followed by refining it through cooperative information exchange with neighbors. This enables an optimized aerodynamic structure that minimizes the formation's overall energy consumption. To ensure control stability and fairness, we formulate a maximum linear quadratic regulator (LQR) minimization problem, which is subject to both the available power budget and the required sensing beam pattern gain. To address this non-convex problem, we develop a two-step approach by first deriving a closed-form expression of LQR as a function of arbitrary beamformers. Subsequently, an efficient iterative algorithm that integrates successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques is proposed to obtain a sub-optimal dual-functional beamforming solution. Extensive simulation results confirm that the 'V'-shaped formation is the most energy-efficient configuration and demonstrate the superiority of our proposed design over benchmark schemes in improving control performance.