Multi-agent deployment under the leader displacement measurement: A PDE-based approach

Jieqiang Wei, Emilia Fridman, Anton Selivanov, Karl H. Johansson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study the deployment of a first-order multiagent system over a desired smooth curve in 3D space. We assume that the agents have access to the local information of the desired curve and their displacements with respect to their closest neighbors, whereas in addition a leader is able to measure his absolute displacement with respect to the desired curve. In this paper we consider the case that the desired curve is a closed mathcal{C}{2} curve and we assume that the leader transmit his measurement to other agents through a communication network. We start the algorithm with displacement-based formation control protocol. Connections from this ODE model to a PDE model (heat equation), which can be seen as a reduced model, are then established. The resulting closed-loop system is modeled as a heat equation with delay (due to the communication). The boundary condition is periodic since the desired curve is closed. By choosing appropriate controller gains (the diffusion coefficient and the gain multiplying the leader state), we can achieve any desired decay rate provided the delay is small enough. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method.

Original languageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783907144008
StatePublished - Jun 2019
Event18th European Control Conference, ECC 2019 - Naples, Italy
Duration: 25 Jun 201928 Jun 2019

Publication series

Name2019 18th European Control Conference, ECC 2019


Conference18th European Control Conference, ECC 2019


FundersFunder number
Stiftelsen för Strategisk Forskning
Knut och Alice Wallenbergs Stiftelse


    • Deployment
    • Distributed parameters systems
    • Lyapunov method
    • Multi-agent systems
    • Time delays


    Dive into the research topics of 'Multi-agent deployment under the leader displacement measurement: A PDE-based approach'. Together they form a unique fingerprint.

    Cite this