Output tracking for a radiative density optical communication system with unknown disturbance

Abstract

This paper deals with boundary tracking problem for a radiative density parabolic equation (RDE) coming from an optical communication system. First, the radiative intensity is modeled by a radiative transfer equation (RTE). The idea of this work is to use the fact that the signal sent by the laser beam is collimated in consideration of the radiative density flux. Therefore, the control problem of the RTE model is transformed into a boundary control for an RDE based on the time-dependent SPN approximation. Then, we investigate a boundary output tracking problem of one dimensional parabolic density equation where the unknown disturbance enters the system from one part of the boundary. By utilizing one side boundary measurement, we construct an extended state observer to estimate the system state and the external disturbance. An output feedback boundary control is then designed using the states of the servo system and observer. It is shown that the closed-loop system and the control are uniformly bounded with output being tracking the reference and the closed-loop is internally exponentially stable. The numerical simulations are presented to illustrate the effectiveness of the proposed output feedback method.