Tracking Control of Optical Beam Transceivers using Mean Field Models

TL;DR

This paper introduces mean field models for optical beam transceiver control in UAV networks, addressing line-of-sight maintenance amidst vibrations, and proposes decentralized and centralized strategies to optimize beam tracking.

Contribution

It develops novel mean field control frameworks for UAV optical transceivers, deriving solutions from advanced differential equations and verifying equilibrium conditions numerically.

Findings

Successful derivation of control strategies using HJB-FP equations

Numerical verification of equilibrium existence and uniqueness

Enhanced UAV network reliability through optimized beam tracking

Abstract

This paper proposes mean field models to maintain an accurate line-of-sight and tracking between transceivers mounted in mobile unmanned aerial vehicles (UAVs) platforms in the presence of underlying mechanical vibration effects. We describe a two-way optical link beam tracking control that coordinates mobile UAVs in a network architecture to provide reliable network structure, distributed connectivity, and communicability, enhancing terrestrial public safety communication systems. We derive the optical transceiver trajectory tracking problem in which each agent dynamic and cost function is coupled with other optical beam transceiver agent states via a mean field term. We propose two optimal mean field beam tracking control frameworks through decentralized and centralized strategies in which the optical transceivers compete to reach a Nash equilibrium and cooperate to attain a social optimum, respectively. The solutions of these strategies are derived from forward-backward ordinary differential equations and rely on the linearity Hamilton-Jacobi-Bellman Fokker-Planck (HJB-FP) equations and stochastic maximum principle. Moreover, we numerically compute the solution pair of the resulting joint equations using Newton and fixed point iteration methods to verify the existence and uniqueness of the equilibrium and social optimum.