The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely, we consider a general class of junction distribution controls and inflow controls and we establish the compactness in L1 of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges
Ancona, F., Cesaroni, A., Coclite, G., Garavello, M. (2018). On the optimization of conservation law models at a junction with inflow and flow distribution controls. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 56(5), 3370-3403 [10.1137/18M1176233].
On the optimization of conservation law models at a junction with inflow and flow distribution controls
Garavello, Mauro
2018
Abstract
The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely, we consider a general class of junction distribution controls and inflow controls and we establish the compactness in L1 of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edgesFile | Dimensione | Formato | |
---|---|---|---|
pubb_3.pdf
Solo gestori archivio
Tipologia di allegato:
Publisher’s Version (Version of Record, VoR)
Dimensione
1.36 MB
Formato
Adobe PDF
|
1.36 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.