TY - GEN
T1 - Well-posedness of networked scalar semilinear balance laws subject to nonlinear boundary control operators
AU - Tang, Shu Xia
AU - Keimer, Alexander
AU - Bayen, Alexandre M.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finite interval. The upstream boundary datum is determined by a nonlinear feedback control operator, representing the fact that traffic routing might be influenced in real time by the traffic information on the entire network. The main contribution of the present work lies in the appropriate design of nonlinear boundary control operators which meanwhile guarantee the well-posedness of the resultant systems. In detail, two different types of specific nonlinear boundary control operators are instantiated, one being Lipschitz continuous and taking into account traffic information from initial time up to present time, one using only delayed traffic information. This contribution thus presents simplified road traffic network dynamics where routing at intersections is dependent of the status of the entire network, incorporating also different classes of traffic flow.
AB - Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finite interval. The upstream boundary datum is determined by a nonlinear feedback control operator, representing the fact that traffic routing might be influenced in real time by the traffic information on the entire network. The main contribution of the present work lies in the appropriate design of nonlinear boundary control operators which meanwhile guarantee the well-posedness of the resultant systems. In detail, two different types of specific nonlinear boundary control operators are instantiated, one being Lipschitz continuous and taking into account traffic information from initial time up to present time, one using only delayed traffic information. This contribution thus presents simplified road traffic network dynamics where routing at intersections is dependent of the status of the entire network, incorporating also different classes of traffic flow.
KW - Semilinear balance law
KW - boundary control
KW - delay
KW - routing
KW - traffic flow
UR - http://www.scopus.com/inward/record.url?scp=85082471331&partnerID=8YFLogxK
U2 - 10.1109/CDC40024.2019.9030172
DO - 10.1109/CDC40024.2019.9030172
M3 - Conference contribution
AN - SCOPUS:85082471331
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4011
EP - 4016
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
Y2 - 11 December 2019 through 13 December 2019
ER -