Distributed Source Seeking for Uncertain Networked Euler–Lagrange Systems over Unbalanced Directed Communication Topologies

This paper investigates the distributed source seeking problem for uncertain networked Euler–Lagrange (EL) systems over unbalanced directed communication topologies. The objective is to drive all agents towards the source of aggregated multiple unknown scalar fields. To achieve this, a novel distributed control protocol is proposed, which consists of three components: a distributed estimator for estimating the left eigenvector of the Laplacian matrix associated with the zero eigenvalue, a distributed optimizer for generating a virtual reference trajectory towards the source, and a trajectory tracker for exponentially driving each agent towards the reference trajectory. By employing the exponential trajectory tracker, the stochastic extremum seeking technique can be effectively integrated into our optimizer tailored for unbalanced directed topologies. By applying the stochastic averaging theory, the weakly exponential convergence of the control protocol can be achieved. Finally, the effectiveness of the proposed distributed control protocol is demonstrated by a numerical example. © 2014 IEEE.