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Spoofing cyber attack detection in probebased traffic monitoring systems using mixed integer linear programming
1.  King Abdullah University of Science and Technology, Electrical Engineering Department, Thuwal, Makkah 23955, KSA, Saudi Arabia, Saudi Arabia 
2.  University of California at Berkely, Electrical Engineering and Computer Sciences, Berkeley CA 94720170 
References:
[1] 
S. Amin, A. Cardenas and S. Sastry, Safe and secure networked control systems under denialofservice attacks, in "Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control," SpringerVerlag, (2009), 3145. doi: 10.1007/9783642006029_3. 
[2] 
S. Amin, X. Litrico, S. Sastry and A. Bayen, Stealthy deception attacks on water scada systems, In "Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control," ACM, (2010),161170. doi: 10.1145/1755952.1755976. 
[3] 
J.P. Aubin, "Viability Theory," Systems and Control: Foundations and Applications, Birkhäuser, Boston, MA, 1991. 
[4] 
J.P. Aubin, A. M. Bayen and P. SaintPierre, Dirichlet problems for some HamiltonJacobi equations with inequality constraints, SIAM Journal on Control and Optimization, 47 (2008), 23482380. doi: 10.1137/060659569. 
[5] 
M. Bardi and I. CapuzzoDolcetta, "Optimal Control and Viscosity Solutions of {HamiltonJacobiBellman} Equations," Birkhäuser, Boston, MA, 1997. doi: 10.1007/9780817647551. 
[6] 
E. N. Barron and R. Jensen, Semicontinuous viscosity solutions for HamiltonJacobi equations with convex Hamiltonians, Communications in Partial Differential Equations, 15 (1990), 17131742. doi: 10.1080/03605309908820745. 
[7] 
E. S. Canepa and C. G. Claudel, Exact solutions to traffic density estimation problems involving the LighthillWhitmanRichards traffic flow model using Mixed Integer Linear Programing, In "Proceedings of the 15th International IEEE Conference on Intelligent Transportation Systems", (2012), 832839. 
[8] 
P. D. Christofides, "Nonlinear and Robust Control of Partial Differential Equation Systems: Methods and Applications to TransportReaction Processes," Birkhäuser, Boston, MA, 2001. doi: 10.1007/9781461201854. 
[9] 
C. G. Claudel and A. M. Bayen, LaxHopf based incorporation of internal boundary conditions into HamiltonJacobi equation. Part I: Theory, IEEE Transactions on Automatic Control, 55 (2010), 11421157. doi: 10.1109/TAC.2010.2041976. 
[10] 
C. G. Claudel and A. M. Bayen, LaxHopf based incorporation of internal boundary conditions into HamiltonJacobi equation. Part {II: Computational methods}, IEEE Transactions on Automatic Control, 55 (2010), 11581174. doi: 10.1109/TAC.2010.2045439. 
[11] 
C. G. Claudel and A. M Bayen, Convex formulations of data assimilation problems for a class of HamiltonJacobi equations, SIAM Journal on Control and Optimization, 49 (2011), 383402. doi: 10.1137/090778754. 
[12] 
M. G. Crandall and P.L. Lions, Viscosity solutions of {HamiltonJacobi equations}, Transactions of the American Mathematical Society, 277 (1983), 142. doi: 10.1090/S00029947198306900398. 
[13] 
C. Daganzo, The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research, 28B (1994), 269287. doi: 10.1016/01912615(94)900027. 
[14] 
C. F. Daganzo, A variational formulation of kinematic waves: basic theory and complex boundary conditions, Transportation Research B, 39B (2005), 187196. doi: 10.1016/j.trb.2004.04.003. 
[15] 
C. F. Daganzo, On the variational theory of traffic flow: wellposedness, duality and applications, Networks and Heterogeneous Media, 1 (2006), 601619. doi: 10.3934/nhm.2006.1.601. 
[16] 
H. Frankowska, Lower semicontinuous solutions of HamiltonJacobiBellman equations, SIAM Journal of Control and Optimization, 31 (1993), 257272. doi: 10.1137/0331016. 
[17] 
J. C. Herrera, D. B. Work, R. Herring, X. J. Ban, Q. Jacobson and A. M. Bayen, Evaluation of traffic data obtained via GPSenabled mobile phones: The Mobile Century field experiment, Transportation Research Part C: Emerging Technologies, 18 (2010), 568583. doi: 10.1016/j.trc.2009.10.006. 
[18] 
B. Hoh, M. Gruteser, R. Herring, J. Ban, D. Work, J. C. Herrera, A. M. Bayen, M. Annavaram and Q. Jacobson, Virtual trip lines for distributed privacypreserving traffic monitoring, in "Proceedings of the 6th International Conference on Mobile Systems, Applications, and Services," ACM, (2008), 1528. doi: 10.1145/1378600.1378604. 
[19] 
M. Krstic and A. Smyshlyaev, Backstepping boundary control for firstorder hyperbolic pdes and application to systems with actuator and sensor delays, Systems & Control Letters, 57 (2008), 750758. doi: 10.1016/j.sysconle.2008.02.005. 
[20] 
P. E. Mazare, A. Dehwah, C. G. Claudel and A. M. Bayen, Analytical and gridfree solutions to the lighthillwhithamrichards traffic flow model, Transportation Research Part B: Methodological, 45 (2011), 17271748. doi: 10.1016/j.trb.2011.07.004. 
[21] 
K. Moskowitz, Discussion of "freeway level of service as influenced by volume and capacity characteristics' by D.R. Drew and C. J. Keese, Highway Research Record, 99 (1965), 4344. 
[22] 
G. F. Newell, A simplified theory of kinematic waves in highway traffic, Part (I), (II) and (III). Transporation Research B, 27B (1993), 281313. 
[23] 
R. C. Smith and M. A. Demetriou, "Research Directions in Distributed Parameter Systems," SIAM, Philadelphia, PA, 2000. doi: 10.1137/1.9780898717525. 
[24] 
I. S. Strub and A. M. Bayen, Weak formulation of boundary conditions for scalar conservation laws, International Journal of Robust and Nonlinear Control, 16 (2006), 733748. doi: 10.1002/rnc.1099. 
[25] 
D. Work, S. Blandin, O. Tossavainen, B. Piccoli and A. Bayen, A distributed highway velocity model for traffic state reconstruction, Applied Research Mathematics eXpress (ARMX), 1 (2010), 135. 
[26]  
[27] 
show all references
References:
[1] 
S. Amin, A. Cardenas and S. Sastry, Safe and secure networked control systems under denialofservice attacks, in "Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control," SpringerVerlag, (2009), 3145. doi: 10.1007/9783642006029_3. 
[2] 
S. Amin, X. Litrico, S. Sastry and A. Bayen, Stealthy deception attacks on water scada systems, In "Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control," ACM, (2010),161170. doi: 10.1145/1755952.1755976. 
[3] 
J.P. Aubin, "Viability Theory," Systems and Control: Foundations and Applications, Birkhäuser, Boston, MA, 1991. 
[4] 
J.P. Aubin, A. M. Bayen and P. SaintPierre, Dirichlet problems for some HamiltonJacobi equations with inequality constraints, SIAM Journal on Control and Optimization, 47 (2008), 23482380. doi: 10.1137/060659569. 
[5] 
M. Bardi and I. CapuzzoDolcetta, "Optimal Control and Viscosity Solutions of {HamiltonJacobiBellman} Equations," Birkhäuser, Boston, MA, 1997. doi: 10.1007/9780817647551. 
[6] 
E. N. Barron and R. Jensen, Semicontinuous viscosity solutions for HamiltonJacobi equations with convex Hamiltonians, Communications in Partial Differential Equations, 15 (1990), 17131742. doi: 10.1080/03605309908820745. 
[7] 
E. S. Canepa and C. G. Claudel, Exact solutions to traffic density estimation problems involving the LighthillWhitmanRichards traffic flow model using Mixed Integer Linear Programing, In "Proceedings of the 15th International IEEE Conference on Intelligent Transportation Systems", (2012), 832839. 
[8] 
P. D. Christofides, "Nonlinear and Robust Control of Partial Differential Equation Systems: Methods and Applications to TransportReaction Processes," Birkhäuser, Boston, MA, 2001. doi: 10.1007/9781461201854. 
[9] 
C. G. Claudel and A. M. Bayen, LaxHopf based incorporation of internal boundary conditions into HamiltonJacobi equation. Part I: Theory, IEEE Transactions on Automatic Control, 55 (2010), 11421157. doi: 10.1109/TAC.2010.2041976. 
[10] 
C. G. Claudel and A. M. Bayen, LaxHopf based incorporation of internal boundary conditions into HamiltonJacobi equation. Part {II: Computational methods}, IEEE Transactions on Automatic Control, 55 (2010), 11581174. doi: 10.1109/TAC.2010.2045439. 
[11] 
C. G. Claudel and A. M Bayen, Convex formulations of data assimilation problems for a class of HamiltonJacobi equations, SIAM Journal on Control and Optimization, 49 (2011), 383402. doi: 10.1137/090778754. 
[12] 
M. G. Crandall and P.L. Lions, Viscosity solutions of {HamiltonJacobi equations}, Transactions of the American Mathematical Society, 277 (1983), 142. doi: 10.1090/S00029947198306900398. 
[13] 
C. Daganzo, The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research, 28B (1994), 269287. doi: 10.1016/01912615(94)900027. 
[14] 
C. F. Daganzo, A variational formulation of kinematic waves: basic theory and complex boundary conditions, Transportation Research B, 39B (2005), 187196. doi: 10.1016/j.trb.2004.04.003. 
[15] 
C. F. Daganzo, On the variational theory of traffic flow: wellposedness, duality and applications, Networks and Heterogeneous Media, 1 (2006), 601619. doi: 10.3934/nhm.2006.1.601. 
[16] 
H. Frankowska, Lower semicontinuous solutions of HamiltonJacobiBellman equations, SIAM Journal of Control and Optimization, 31 (1993), 257272. doi: 10.1137/0331016. 
[17] 
J. C. Herrera, D. B. Work, R. Herring, X. J. Ban, Q. Jacobson and A. M. Bayen, Evaluation of traffic data obtained via GPSenabled mobile phones: The Mobile Century field experiment, Transportation Research Part C: Emerging Technologies, 18 (2010), 568583. doi: 10.1016/j.trc.2009.10.006. 
[18] 
B. Hoh, M. Gruteser, R. Herring, J. Ban, D. Work, J. C. Herrera, A. M. Bayen, M. Annavaram and Q. Jacobson, Virtual trip lines for distributed privacypreserving traffic monitoring, in "Proceedings of the 6th International Conference on Mobile Systems, Applications, and Services," ACM, (2008), 1528. doi: 10.1145/1378600.1378604. 
[19] 
M. Krstic and A. Smyshlyaev, Backstepping boundary control for firstorder hyperbolic pdes and application to systems with actuator and sensor delays, Systems & Control Letters, 57 (2008), 750758. doi: 10.1016/j.sysconle.2008.02.005. 
[20] 
P. E. Mazare, A. Dehwah, C. G. Claudel and A. M. Bayen, Analytical and gridfree solutions to the lighthillwhithamrichards traffic flow model, Transportation Research Part B: Methodological, 45 (2011), 17271748. doi: 10.1016/j.trb.2011.07.004. 
[21] 
K. Moskowitz, Discussion of "freeway level of service as influenced by volume and capacity characteristics' by D.R. Drew and C. J. Keese, Highway Research Record, 99 (1965), 4344. 
[22] 
G. F. Newell, A simplified theory of kinematic waves in highway traffic, Part (I), (II) and (III). Transporation Research B, 27B (1993), 281313. 
[23] 
R. C. Smith and M. A. Demetriou, "Research Directions in Distributed Parameter Systems," SIAM, Philadelphia, PA, 2000. doi: 10.1137/1.9780898717525. 
[24] 
I. S. Strub and A. M. Bayen, Weak formulation of boundary conditions for scalar conservation laws, International Journal of Robust and Nonlinear Control, 16 (2006), 733748. doi: 10.1002/rnc.1099. 
[25] 
D. Work, S. Blandin, O. Tossavainen, B. Piccoli and A. Bayen, A distributed highway velocity model for traffic state reconstruction, Applied Research Mathematics eXpress (ARMX), 1 (2010), 135. 
[26]  
[27] 
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