Network-based deployment of the second-order multi agents: A PDE approach

Maria Terushkin*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Deployment of a second-order nonlinear multi agent system over a desired open smooth curve in 2D or 3D space is considered. We assume that the agents have access to their velocities and 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 position. We assume that a small number of leaders transmit their measurements to other agents through a communication network. We take into account the following network imperfections: the variable sampling, transmission delay and quantization. We propose a static output-feedback controller and model the resulting closed-loop system as a disturbed (due to quantization) nonlinear damped wave equation with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. To manage with the open curve we consider Neumann boundary conditions. We derive linear matrix inequalities (LMIs) that guarantee the input-to-state stability (ISS) of the system. 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
Pages (from-to)7617-7622
Number of pages6
Issue number2
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 12 Jul 202017 Jul 2020


  • Distributed parameter systems
  • Multi-agent systems
  • Network-based control
  • Time-delay


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