Backstepping-based extended Luenberger observer design for a Burgers-type PDE for multi-agent deployment

Abstract

An extended Luenberger state observer is presented for a Burgers-type PDE. For this, pointwise boundary and an additional in-domain measurement are considered, which allows to split the observer setup into two subsystems. The observer gains are determined by utilizing the backstepping technique, which enables to stabilize the distributed parameter observer error dynamics. The concept is integrated into a motion planning and feedback control strategy and is applied to achieve the deployment of multi-agent continuum into desired spatial-temporal formation profiles. For the evaluation of the observer strategy the transfer to a finite-dimensional discrete multi-agent system in leader-follower configuration is obtained by means of a finite difference discretization. This in addition imposes the required communication topology for the interconnected agents.