Distributed Consensus of Networked Lagrangian Systems With Unknown Nonidentical Control Directions

Yunfeng Ji,Jianwei Zhang,Gang Wang,Qingdu Li,Na Liu,Song Tang

doi:10.1109/access.2020.2976903

Abstract

In the literature, most of the consensus methods require the control directions of all agents to be known. This paper deals with the distributed consensus problem without such requirements for networked Lagrangian systems subjected to uncertain dynamics. Unknown control directions are nonidentical in the sense that the control direction related to each control input in an individual Lagrangian system can be different and unknown as well as that the control directions for different Lagrangian systems are allowed to be distinct. Regarding the communication topology, the only requirement is to contain a fixed directed spanning tree. Based on the estimated consensus value, novel auxiliary sliding mode variables are constructed and applied to develop the distributed adaptive consensus control scheme. It is proved by adopting the special properties of the Laplacian matrix on directed graphs and matrix theory that global uniform boundedness of all closed-loop signals and the asymptotic consensus can be achieved. Simulations on networked two-link revolute joint arms are provided to verify the validity of the proposed scheme.

Highlights

Over the past few years, distributed consensus control of multi-agent systems has received considerable attention in the control community due to its wide potential applications
MAIN RESULTS we present a distributed adaptive consensus controller for networked Lagrangian systems in the presence of uncertain dynamics and unknown nonidentical control directions
Inspired by [25], the main idea of the derivation is to construct a new auxiliary sliding mode variable based on the estimated consensus value, so that the difficulty encountered in [21]–[24] that a holistic conditional inequality ensuring closed-loop stability and asymptotic convergence has to be established for the entire multi-agent systems can be overcome

Summary

Introduction

Over the past few years, distributed consensus control of multi-agent systems has received considerable attention in the control community due to its wide potential applications. Compared with the control of a single system, significant challenges in the distributed consensus of multi-agent systems lie in the restriction that designing controllers depends solely on local information exchanges to reach a global consensus, immediately resulting in more complex-structured algorithms [1], [2]. Much attention has been paid to distributed control of single and double integrator systems [3]–[6]. Numerous practical engineering systems exist failing to be represented using such models and should be described by Lagrangian equations; see, for instance, mobile robots [7], robotic manipulators [8], and surface vessels [9]. Designing distributed control schemes for networked Lagrangian systems is of great importance.

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Conclusion