PDE-Based Deployment of Multiagents Measuring Relative Position to One Neighbor
Anton Selivanov, Emilia Fridman
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.
Topics & Concepts
Partial differential equationPosition (finance)DiscretizationSoftware deploymentStability (learning theory)Lyapunov functionComputer scienceMathematical optimizationFunction (biology)Control theory (sociology)Applied mathematicsMathematicsArtificial intelligenceMathematical analysisControl (management)PhysicsMachine learningOperating systemEconomicsEvolutionary biologyNonlinear systemFinanceQuantum mechanicsBiologyMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern FormationStability and Controllability of Differential Equations