PDE-Based Deployment of Multiagents Measuring Relative Position to One Neighbor

Anton Selivanov; Emilia Fridman

doi:10.1109/LCSYS.2022.3169999

PDE-Based Deployment of Multiagents Measuring Relative Position to One Neighbor

Anton Selivanov^*, Emilia Fridman

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a PDE-based approach to multi-agent deployment where each agent measures its relative position to only one neighbor. First, we show that such systems can be modeled by a first-order hyperbolic partial differential equation (PDE) whose L2-stability implies the stability of the multi-agent system for a large enough number of agents. Then, we show that PDE modelling helps to construct a Lyapunov function for the multi-agent system using spatial discretisation. Then, we use the PDE model to estimate the leader input delay preserving the stability.

Original language	English
Pages (from-to)	2563-2568
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	6
DOIs	https://doi.org/10.1109/LCSYS.2022.3169999
State	Published - 2022

Keywords

Linear matrix inequalities
Multi-agent systems
Partial differential equations
Time-delay systems

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10.1109/LCSYS.2022.3169999

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abstract = "We develop a PDE-based approach to multi-agent deployment where each agent measures its relative position to only one neighbor. First, we show that such systems can be modeled by a first-order hyperbolic partial differential equation (PDE) whose L2-stability implies the stability of the multi-agent system for a large enough number of agents. Then, we show that PDE modelling helps to construct a Lyapunov function for the multi-agent system using spatial discretisation. Then, we use the PDE model to estimate the leader input delay preserving the stability.",

keywords = "Linear matrix inequalities, Multi-agent systems, Partial differential equations, Time-delay systems",

author = "Anton Selivanov and Emilia Fridman",

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AB - We develop a PDE-based approach to multi-agent deployment where each agent measures its relative position to only one neighbor. First, we show that such systems can be modeled by a first-order hyperbolic partial differential equation (PDE) whose L2-stability implies the stability of the multi-agent system for a large enough number of agents. Then, we show that PDE modelling helps to construct a Lyapunov function for the multi-agent system using spatial discretisation. Then, we use the PDE model to estimate the leader input delay preserving the stability.

KW - Linear matrix inequalities

KW - Multi-agent systems

KW - Partial differential equations

KW - Time-delay systems

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JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

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PDE-Based Deployment of Multiagents Measuring Relative Position to One Neighbor

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