A P ] 2 5 Fe b 20 08 Modeling and Optimal Control of Networks of Pipes and Canals February 25 , 2008

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an optimal control is proved. From the analytical point of view, these results are based on the well posedness of a suitable initial boundary value problem and on techniques for quasidifferential equations in a metric space.

[1]  J. Goodman.  Initial boundary value problems for hyperbolic systems of conservation laws , 1982 .

[2]  Andrezej J. Osiadacz.  Dynamic Optimization of High Pressure Gas Networks Using Hierarchical Systems Theory , 1994 .

[3]  H. Holden,et al.  A mathematical model of traffic flow on a network of unidirectional roads , 1995 .

[4]  R. Colombo,et al.  Continuous Dependence for 2×2 Conservation Laws with Boundary , 1997 .

[5]  D. Amadori.  Initial-boundary value problems for nonlinear systems of conservation laws , 1997 .

[6]  R. Colombo,et al.  Viscosity solutions and standard Riemann semigroup for conservation laws with boundary , 1998 .

[7]  A. Bressan,et al.  L1 Stability Estimates for n×n Conservation Laws , 1999 .

[8]  D. Serre.  Systems of conservation laws , 1999 .

[9]  Tai-Ping Liu,et al.  A NEW ENTROPY FUNCTIONAL FOR A SCALAR CONSERVATION LAW , 1999 .

[10]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[11]  Tai-Ping Liu,et al.  Well‐posedness theory for hyperbolic conservation laws , 1999 .

[12]  H. Holden,et al.  Riemann problems with a kink , 1999 .

[13]  G. Guerra,et al.  Uniqueness and Continuous Dependence for Systems of Balance Laws with Dissipation , 2001 .

[14]  Günter Leugering,et al.  Modelling, Stabilization, and Control of Flow in Networks of Open Channels , 2001 .

[15]  Guenter Leugering,et al.  On the Modelling and Stabilization of Flows in Networks of Open Canals , 2002, SIAM J. Control. Optim..

[16]  Günter Leugering,et al.  Global boundary controllability of the de St. Venant equations between steady states , 2003 .

[17]  Ta-Tsien Li,et al.  Exact Boundary Controllability for Quasi-Linear Hyperbolic Systems , 2002, SIAM J. Control. Optim..

[18]  Jonathan de Halleux,et al.  Boundary feedback control in networks of open channels , 2003, Autom..

[19]  Marc C. Steinbach,et al.  Nonlinear Optimization in Gas Networks , 2003, HPSC.

[20]  Tatsien Li,et al.  Exact Boundary Controllability of Unsteady Flows in a Tree-like Network of Open Canals , 2004 .

[21]  M. Gugat,et al.  Global controllability between steady supercritical flows in channel networks , 2004 .

[22]  Rinaldo M. Colombo,et al.  Minimising stop and go waves to optimise traffic flow , 2004, Appl. Math. Lett..

[23]  Li Tatsien.  Exact controllability for quasilinear hyperbolic systems and its application to unsteady flows in a network of open canals , 2004 .

[24]  Martin Gugat,et al.  Nodal Control of Conservation Laws On Networks , 2005 .

[25]  E. Shashi Menon,et al.  Gas pipeline hydraulics , 2005 .

[26]  Alexander Martin,et al.  Mixed Integer Models for the Stationary Case of Gas Network Optimization , 2006, Math. Program..

[27]  Axel Klar,et al.  Coupling conditions for gas networks governed by the isothermal Euler equations , 2006, Networks Heterog. Media.

[28]  CIRO D’APICE,et al.  Packet Flow on Telecommunication Networks , 2006, SIAM J. Math. Anal..

[29]  Mauro Garavello,et al.  A Well Posed Riemann Problem for the p-System at a Junction , 2006, Networks Heterog. Media.

[30]  Axel Klar,et al.  Gas flow in pipeline networks , 2006, Networks Heterog. Media.

[31]  R. Colombo,et al.  Differential Equations in Metric Spaces with Applications , 2007, 0712.0560.

[32]  R. Colombo,et al.  On the Stability Functional for Conservation Laws , 2007, 0704.2491.

[33]  R. Colombo,et al.  Hyperbolic Balance Laws with a Non Local Source , 2007, 0704.2031.

[34]  A. Marson,et al.  Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws , 2007 .

[35]  R. Colombo,et al.  Hyperbolic Balance Laws with a Dissipative Non Local Source , 2007, 0712.1555.

[36]  M. Steinbach.  On PDE solution in transient optimization of gas networks , 2007 .

[37]  Mauro Garavello,et al.  On the Cauchy Problem for the p-System at a Junction , 2008, SIAM J. Math. Anal..

[38]  Michael Herty,et al.  On 2˟2 Conservation Laws at a Junction , 2008, SIAM J. Math. Anal..

[39]  Marc C. Steinbach,et al.  Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks , 2009 .

[40]  Marc C. Steinbach,et al.  Optimization models for operative planning in drinking water networks , 2009 .