Computationally Efficient Control for Cooperative Optical Beam Tracking With Guaranteed Finite-Time Convergence

Achieving and maintaining line-of-sight (LOS) is an essential attribute for free-space optical (FSO) communication systems as the optical signals are highly directional. We consider the problem of achieving LOS between two agents in a planar setting. We model the underlying agent motion as a discrete-time dynamical system. Each agent seeks to maximize its own output (measurement) function that depends on the states (orientations) of both agents, and furthermore, the agents are required to simultaneously make their moves. Since the output functions are nonconflicting, the beam tracking problem is inherently cooperative; improving one output function concurrently optimizes the other. Nonetheless, challenges arise from the lack of communication between the agents, the absence of state information, and the requirement for simultaneous actions. We propose a novel computationally efficient output feedback control algorithm meeting all these constraints. In particular, we establish that when the level sets of the output functions satisfy certain conditions, the proposed control procedure guarantees that, in a finite number of steps, the system reaches a limiting set that contains the global optimum. The size of this limiting set is proportional to the step size. Simulation results based on an FSO communication setup demonstrate the efficacy of the approach and establish its superiority over two competing approaches, namely the classical extremum seeking control approach and an approach based on the use of an extended Kalman filter, in terms of convergence speed and robustness to disturbance. Experimental results on a setup involving two robots further validate the efficacy and quantify the proposed approach’s performance.