Optimal and Feedback Control for Hyperbolic Conservation Laws

[1]  Nagel.  Particle hopping models and traffic flow theory. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Sylvie Benzoni-Gavage,et al.  Multi-dimensional hyperbolic partial differential equations , 2006 .

[3]  H. M. Zhang.  A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR , 2002 .

[4]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Axel Klar,et al.  Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic , 2000, SIAM J. Appl. Math..

[6]  Pushkin Kachroo,et al.  A Microscopic-To-Macroscopic Crowd Dynamic Model , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[7]  L. A. Pipes.  An Operational Analysis of Traffic Dynamics , 1953 .

[8]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[9]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[10]  A. Bressan.  Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem , 2000 .

[11]  H. Greenberg.  An Analysis of Traffic Flow , 1959 .

[12]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[13]  Michel Rascle,et al.  Resurrection of "Second Order" Models of Traffic Flow , 2000, SIAM J. Appl. Math..

[14]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[15]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[16]  R. Bartle.  The elements of integration and Lebesgue measure , 1995 .

[17]  Denos C. Gazis,et al.  The Origins of Traffic Theory , 2002, Oper. Res..

[18]  Stefan Ulbrich,et al.  Adjoint-based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws , 2003, Syst. Control. Lett..

[19]  Evacuation Dynamics,et al.  Pedestrian and evacuation dynamics 2005 , 2007 .

[20]  D. Kröner.  Numerical Schemes for Conservation Laws , 1997 .

[21]  Ning Zhao,et al.  Conservative front tracking and level set algorithms , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[22]  I. N. Sneddon,et al.  Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves , 1999 .

[23]  Mauro Garavello,et al.  Traffic Flow on Networks , 2006 .

[24]  Sylvie Benzoni-Gavage,et al.  Multidimensional hyperbolic partial differential equations : first-order systems and applications , 2006 .

[25]  Sabiha Amin Wadoo,et al.  Feedback Control Design and Stability Analysis of One Dimensional Evacuation System , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[26]  John M. Watts,et al.  Computer models for evacuation analysis , 1987 .

[27]  Kaan Ozbay,et al.  Feedback Control Theory for Dynamic Traffic Assignment , 1998 .

[28]  S. Ulbrich.  Optimal control of nonlinear hyperbolic conservation laws with source terms , 2001 .

[29]  Issam S. Strub,et al.  Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling , 2006 .

[30]  Markos Papageorgiou,et al.  Applications of Automatic Control Concepts to Traffic Flow Modeling and Control , 1983 .

[31]  Hector O. Fattorini,et al.  Infinite Dimensional Optimization and Control Theory: References , 1999 .

[32]  Sabiha Amin Wadoo,et al.  Feedback control design and stability analysis of two dimensional evacuation system , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[33]  Sabiha Amin Wadoo,et al.  Evacuation Distributed Feedback Control and Abstraction , 2007 .

[34]  C. Dafermos.  Polygonal approximations of solutions of the initial value problem for a conservation law , 1972 .

[35]  Robert Herman,et al.  Kinetic theory of vehicular traffic , 1971 .

[36]  R. Rogers,et al.  An introduction to partial differential equations , 1993 .

[37]  Kaan Ozbay,et al.  System dynamics and feedback control problem formulations for real time dynamic traffic routing , 1998 .

[38]  J. Málek.  Weak and Measure-valued Solutions to Evolutionary PDEs , 1996 .

[39]  Felix Otto,et al.  Initial-boundary value problem for a scalar conservation law , 1996 .

[40]  Lucien W. Neustadt,et al.  Optimization: A Theory of Necessary Conditions , 1976 .

[41]  C. Daganzo.  Requiem for second-order fluid approximations of traffic flow , 1995 .

[42]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[43]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[44]  D. Gazis,et al.  Nonlinear Follow-the-Leader Models of Traffic Flow , 1961 .

[45]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[46]  Peter D. Lax,et al.  Hyperbolic Partial Differential Equations , 2004 .

[47]  Tong Li,et al.  L 1 stability of conservation laws for a traffic flow model ∗ , 2001 .

[48]  G. Folland.  Introduction to Partial Differential Equations , 1976 .

[49]  H. Holden,et al.  Front Tracking for Hyperbolic Conservation Laws , 2002 .

[50]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[51]  E. Montroll,et al.  Traffic Dynamics: Studies in Car Following , 1958 .

[52]  Joseph L. Schofer,et al.  A STATISTICAL ANALYSIS OF SPEED-DENSITY HYPOTHESES , 1965 .

[53]  M J Lighthill,et al.  ON KINEMATIC WAVES.. , 1955 .

[54]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[55]  H. M. Zhang.  A theory of nonequilibrium traffic flow , 1998 .

[56]  I. P. Natanson,et al.  Theory of Functions of a Real Variable , 1955 .

[57]  Richard Courant,et al.  Supersonic Flow And Shock Waves , 1948 .

[58]  Bernardo Cockburn,et al.  On Convergence to Entropy Solutions of A Single Conservation Law , 1996 .

[59]  Jaroslaw Was,et al.  Cellular automata model of pedestrian dynamics for normal and evacuation conditions , 2005, 5th International Conference on Intelligent Systems Design and Applications (ISDA'05).

[60]  N. Risebro.  A front-tracking alternative to the random choice method , 1993 .

[61]  M. Rascle.  An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model , 2002 .

[62]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[63]  R. B. Potts,et al.  Car-Following Theory of Steady-State Traffic Flow , 1959 .

[64]  P. Kachroo,et al.  Isolated ramp metering feedback control utilizing mixed sensitivity for desired mainline density and the ramp queues , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[65]  Z. Xin,et al.  The relaxation schemes for systems of conservation laws in arbitrary space dimensions , 1995 .

[66]  A. Fursikov.  Optimal Control of Distributed Systems: Theory and Applications , 2000 .

[67]  P. Lax.  Hyperbolic systems of conservation laws , 2006 .

[68]  Sadeq J. Al-nasur.  New Models for Crowd Dynamics and Control , 2006 .

[69]  W. Rudin.  Principles of mathematical analysis , 1964 .

[70]  Donald Richard Drew,et al.  Traffic flow theory and control , 1968 .

[71]  J. Glimm.  Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[72]  Adolf D. May,et al.  Traffic Flow Fundamentals , 1989 .

[73]  L. Holden,et al.  A NUMERICAL METHOD FOR FIRST ORDER NONLINEAR SCALAR CONSERVATION LAWS IN ONE-DIMENSION , 1988 .

[74]  Pushkin Kachroo,et al.  Robust Feedback Control of a Single Server Queueing System , 1999, Math. Control. Signals Syst..

[75]  L. Chambers.  Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

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

[77]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[78]  Tong Li,et al.  Global Solutions and Zero Relaxation Limit for a Traffic Flow Model , 2000, SIAM J. Appl. Math..

[79]  J. Nédélec,et al.  First order quasilinear equations with boundary conditions , 1979 .

[80]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[81]  C. Dafermos.  Hyberbolic Conservation Laws in Continuum Physics , 2000 .

[82]  A. V. Fursikov,et al.  Optimal control of distributed systems , 1999 .