TY - JOUR

T1 - Network-based deployment of nonlinear multi agents over open curves

T2 - A PDE approach

AU - Terushkin, Maria

AU - Fridman, Emilia

N1 - Publisher Copyright:
© 2021 Elsevier Ltd

PY - 2021/7

Y1 - 2021/7

N2 - Deployment of the first-order and second-order nonlinear multi agent systems over desired open (and, as a particular case, closed) smooth curves in 2D or 3D space is considered. The considered nonlinearities are globally Lipschitz. We assume that the agents have access to the local information of the desired curve and to their positions with respect to their closest neighbors (as well as to their velocities for the second-order systems), whereas in addition a leader agent is able to measure its absolute position. We assume that a small number of leaders (distributed in the spatial domain) transmit their measurements to other agents through a communication network. We take into account the following network imperfections: 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 heat equation (for the first-order systems) or damped wave equation (for the second-order systems) with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. In order to cope with the open curve we consider Neumann boundary conditions that ensure mobility of the boundary agents. 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 examples illustrate the efficiency of the method.

AB - Deployment of the first-order and second-order nonlinear multi agent systems over desired open (and, as a particular case, closed) smooth curves in 2D or 3D space is considered. The considered nonlinearities are globally Lipschitz. We assume that the agents have access to the local information of the desired curve and to their positions with respect to their closest neighbors (as well as to their velocities for the second-order systems), whereas in addition a leader agent is able to measure its absolute position. We assume that a small number of leaders (distributed in the spatial domain) transmit their measurements to other agents through a communication network. We take into account the following network imperfections: 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 heat equation (for the first-order systems) or damped wave equation (for the second-order systems) with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. In order to cope with the open curve we consider Neumann boundary conditions that ensure mobility of the boundary agents. 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 examples illustrate the efficiency of the method.

KW - Distributed parameter systems

KW - Multi-agent systems

KW - Network-based control

KW - Time-delay

UR - http://www.scopus.com/inward/record.url?scp=85105302142&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2021.109697

DO - 10.1016/j.automatica.2021.109697

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AN - SCOPUS:85105302142

SN - 0005-1098

VL - 129

JO - Automatica

JF - Automatica

M1 - 109697

ER -