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Jamming in mobile networks: A gametheoretic approach
Safe and reliable coverage control
1.  Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering, University of Illinois at UrbanaChampaign, Urbana, Illinois, United States 
2.  Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, California, United States 
3.  Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, California, United States 
References:
[1] 
A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2^{nd}edition, SpringerVerlag, Berlin, Germany, 2005. 
[2] 
J. V. Breakwell and P. Hagedorn, Point capture of two evaders in succession, Journal of Optimization Theory and Applications, 27 (1979), 8997. doi: 10.1007/BF00933327. 
[3] 
C. R. Burns, R. F. Wang and D. M. Stipanović, A study of human and receding horizon controller perfomance of a remote navigation task with obstacles and feedback delays, Journal of Behavioral Robotics, 2 (2011), 4463. 
[4] 
F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 312. 
[5] 
N. Chopra, D. M. Stipanovićand M. W. Spong, On synchronization and collision avoidance for mechanical systems, Proceedings of the 2008 American Control Conference, (2008), 37133718. doi: 10.1109/ACC.2008.4587071. 
[6] 
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw Hill, New York, NY, 1955. 
[7] 
M. Corless, G. Leitmann, and J. M. Skowronski, Adaptive control for avoidance or evasion in an uncertain environment, Computers & Mathematics with Applications, 13 (1987), 111. doi: 10.1016/08981221(87)900903. 
[8] 
M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161170. doi: 10.1016/08981221(89)901338. 
[9] 
A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988. 
[10] 
V. V. Filippov, "Basic Topological Structures of Ordinary Differential Equations," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998. 
[11] 
H. Flanders, Differentiation under the integral sign, The American Mathematical Monthly, 80 (1973), 615627. doi: 10.2307/2319163. 
[12] 
R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996. 
[13] 
J. K. Hale and S. M. V. Lunel, "Introduction to Functional Differential Equations," SpringerVerlag, New York, NY, 1993. 
[14] 
P. F. Hokayem, D. M. Stipanović and M. W. Spong, Semiautonomous control of multiple networked Langrangian systems, International Journal of Robust and Nonlinear Control, 19 (2009), 20402055. doi: 10.1002/rnc.1391. 
[15] 
I. I. Hussein and D. M. Stipanović, Effective coverage control for mobile sensor networks with guaranteed collision avoidance, IEEE Transactions on Control Systems Technology, 15 (2007), 642657. doi: 10.1109/TCST.2007.899155. 
[16] 
I. I. Hussein and D. M. Stipanović, Effective coverage control using dynamic sensor networks with flocking and guaranteed collision avoidance, Proceedings of the 2007 American Control Conference, (2007), 34203425. doi: 10.1109/ACC.2007.4282310. 
[17] 
R. Isaacs, "Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization," John Wiley and Sons, Inc., New York, NY, 1965. 
[18] 
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975. 
[19] 
V. Lakshmikantham and S. Leela, "Differential and Integral Inequalities: Theory and Applications," Mathematics in Science and Engineering, vol. 55, Academic Press, New York, NY, 1969. 
[20] 
V. Lakshmikantham, S. Leela and A. A. Martinyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, New York, NY, 1989. 
[21] 
I. B. Lazarević, "Multidimensional Mathematical Analysis," OrionArt, Belgrade, Serbia, 2005. 
[22] 
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581591. doi: 10.1007/BF00933298. 
[23] 
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569576. doi: 10.1007/BF00934040. 
[24] 
G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850851. doi: 10.1109/TAC.1980.1102408. 
[25] 
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335342. doi: 10.1002/oca.4660040406. 
[26] 
S. Mastellone, D. M. Stipanović, C. R. Graunke, K. A. Intlekofer and M. W. Spong, Formation control and collision avoidance for multiagent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107126. doi: 10.1177/0278364907084441. 
[27] 
A. A. Melikyan, The problem of timeoptimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 17. 
[28] 
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998. doi: 10.1007/9781461555636. 
[29] 
I. Mitchell, A. M. Bayen and C. J. Tomlin, A timedependent HamiltonJacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947957. doi: 10.1109/TAC.2005.851439. 
[30] 
L. A. Petrosjan, "Differential Games of Pursuit," Series on Optimization, vol. 2, World Scientific, Singapore, 1993. doi: 10.1142/1670. 
[31] 
E. J. RodríguezSeda, J. J. Troy, C. A. Erignac, P. Murray, D. M. Stipanović and M. W. Spong, Bilateral teleoperation of multiple mobile agents: Formation control and collision avoidance, IEEE Transactions on Control Systems Technology, 18 (2010), 984992. doi: 10.1109/TCST.2009.2030176. 
[32] 
E. J. RodríguezSeda, D. M. Stipanović and M. W. Spong, Collision avoidance control with sensing uncertainties, Proceedings of the 2011 American Control Conference, 2011. 
[33] 
M. Saska, J. S. Mejía, D. M. Stipanović and K. Schilling, Control and navigation of formations of carlike robots on a receding horizon, Proceedings of the 2009 IEEE Multiconference on Systems and Control. St Petersburg, Russia, 2009. 
[34] 
R. Siegwart and I. R. Nourbakhsh, "Introduction to Autonomous Mobile Robots," The MIT Press, Cambridge, Massachusetts, 2004. 
[35] 
D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multiplayer pursuitevasion games, Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, Tucson, Arizona, 2004. 
[36] 
D. M. Stipanović, P. F. Hokayem, M. W. Spong and D. D. Šiljak, Cooperative avoidance control for multiagent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699707. doi: 10.1115/1.2764510. 
[37] 
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multiplayer pursuitevasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133145. 
[38] 
D. M. Stipanović, A survey and some new results in avoidance control, in "Proceedings of the 15th International Workshop on Dynamics and Control," Tossa de Mar, Spain, (2009), 166173. 
[39] 
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multiplayer pursuitevasion games, International Game Theory Review, 12 (2010), 117. doi: 10.1142/S0219198910002489. 
[40] 
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multiobjective problems, Applied Mathematics & Optimization, 66 (2012), 455473. 
[41] 
D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multiobjective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487493. 
[42] 
D. M. Stipanović, C. J. Tomlin and C. Valicka, Collision free coverage control with multiple agents, Proceedings of the RoMoCo'11 Conference, Bukowy Dworek, Poland, 2011. 
[43] 
E. M. Vaisbord and V. I. Zhukovskiy, "Introduction to MultiPlayer Differential Games and Their Applications," Gordon and Breach, New York, NY, 1988. 
[44] 
C. G. Valicka, S. R. Bieniawski, J. Vian, and D. M. Stipanović, Cooperative avoidance control for UAVs, Proceedings of the Tenth International Conference on Control, Automation, Robotics and Vision (ICARCV 2008), Hanoi, Vietnam (2008), 14621468. 
[45] 
T. L. Vincent and W. J. Grantham, "Nonlinear and Optimal Control Systems," John Wiley & Sons, Inc., New York, NY, 1997. 
[46] 
M. M. Zavlanos and G. J. Pappas, Potential fields for maintaining connectivity of mobile networks, IEEE Transactions on Robotics, 23 (2007), 812816. doi: 10.1109/TRO.2007.900642. 
[47] 
V. A. Zorich, "Mathematical Analysis II," SpringerVerlag, Berlin, Germany, 2004. 
show all references
References:
[1] 
A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2^{nd}edition, SpringerVerlag, Berlin, Germany, 2005. 
[2] 
J. V. Breakwell and P. Hagedorn, Point capture of two evaders in succession, Journal of Optimization Theory and Applications, 27 (1979), 8997. doi: 10.1007/BF00933327. 
[3] 
C. R. Burns, R. F. Wang and D. M. Stipanović, A study of human and receding horizon controller perfomance of a remote navigation task with obstacles and feedback delays, Journal of Behavioral Robotics, 2 (2011), 4463. 
[4] 
F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 312. 
[5] 
N. Chopra, D. M. Stipanovićand M. W. Spong, On synchronization and collision avoidance for mechanical systems, Proceedings of the 2008 American Control Conference, (2008), 37133718. doi: 10.1109/ACC.2008.4587071. 
[6] 
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw Hill, New York, NY, 1955. 
[7] 
M. Corless, G. Leitmann, and J. M. Skowronski, Adaptive control for avoidance or evasion in an uncertain environment, Computers & Mathematics with Applications, 13 (1987), 111. doi: 10.1016/08981221(87)900903. 
[8] 
M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161170. doi: 10.1016/08981221(89)901338. 
[9] 
A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988. 
[10] 
V. V. Filippov, "Basic Topological Structures of Ordinary Differential Equations," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998. 
[11] 
H. Flanders, Differentiation under the integral sign, The American Mathematical Monthly, 80 (1973), 615627. doi: 10.2307/2319163. 
[12] 
R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996. 
[13] 
J. K. Hale and S. M. V. Lunel, "Introduction to Functional Differential Equations," SpringerVerlag, New York, NY, 1993. 
[14] 
P. F. Hokayem, D. M. Stipanović and M. W. Spong, Semiautonomous control of multiple networked Langrangian systems, International Journal of Robust and Nonlinear Control, 19 (2009), 20402055. doi: 10.1002/rnc.1391. 
[15] 
I. I. Hussein and D. M. Stipanović, Effective coverage control for mobile sensor networks with guaranteed collision avoidance, IEEE Transactions on Control Systems Technology, 15 (2007), 642657. doi: 10.1109/TCST.2007.899155. 
[16] 
I. I. Hussein and D. M. Stipanović, Effective coverage control using dynamic sensor networks with flocking and guaranteed collision avoidance, Proceedings of the 2007 American Control Conference, (2007), 34203425. doi: 10.1109/ACC.2007.4282310. 
[17] 
R. Isaacs, "Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization," John Wiley and Sons, Inc., New York, NY, 1965. 
[18] 
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975. 
[19] 
V. Lakshmikantham and S. Leela, "Differential and Integral Inequalities: Theory and Applications," Mathematics in Science and Engineering, vol. 55, Academic Press, New York, NY, 1969. 
[20] 
V. Lakshmikantham, S. Leela and A. A. Martinyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, New York, NY, 1989. 
[21] 
I. B. Lazarević, "Multidimensional Mathematical Analysis," OrionArt, Belgrade, Serbia, 2005. 
[22] 
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581591. doi: 10.1007/BF00933298. 
[23] 
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569576. doi: 10.1007/BF00934040. 
[24] 
G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850851. doi: 10.1109/TAC.1980.1102408. 
[25] 
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335342. doi: 10.1002/oca.4660040406. 
[26] 
S. Mastellone, D. M. Stipanović, C. R. Graunke, K. A. Intlekofer and M. W. Spong, Formation control and collision avoidance for multiagent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107126. doi: 10.1177/0278364907084441. 
[27] 
A. A. Melikyan, The problem of timeoptimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 17. 
[28] 
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998. doi: 10.1007/9781461555636. 
[29] 
I. Mitchell, A. M. Bayen and C. J. Tomlin, A timedependent HamiltonJacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947957. doi: 10.1109/TAC.2005.851439. 
[30] 
L. A. Petrosjan, "Differential Games of Pursuit," Series on Optimization, vol. 2, World Scientific, Singapore, 1993. doi: 10.1142/1670. 
[31] 
E. J. RodríguezSeda, J. J. Troy, C. A. Erignac, P. Murray, D. M. Stipanović and M. W. Spong, Bilateral teleoperation of multiple mobile agents: Formation control and collision avoidance, IEEE Transactions on Control Systems Technology, 18 (2010), 984992. doi: 10.1109/TCST.2009.2030176. 
[32] 
E. J. RodríguezSeda, D. M. Stipanović and M. W. Spong, Collision avoidance control with sensing uncertainties, Proceedings of the 2011 American Control Conference, 2011. 
[33] 
M. Saska, J. S. Mejía, D. M. Stipanović and K. Schilling, Control and navigation of formations of carlike robots on a receding horizon, Proceedings of the 2009 IEEE Multiconference on Systems and Control. St Petersburg, Russia, 2009. 
[34] 
R. Siegwart and I. R. Nourbakhsh, "Introduction to Autonomous Mobile Robots," The MIT Press, Cambridge, Massachusetts, 2004. 
[35] 
D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multiplayer pursuitevasion games, Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, Tucson, Arizona, 2004. 
[36] 
D. M. Stipanović, P. F. Hokayem, M. W. Spong and D. D. Šiljak, Cooperative avoidance control for multiagent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699707. doi: 10.1115/1.2764510. 
[37] 
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multiplayer pursuitevasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133145. 
[38] 
D. M. Stipanović, A survey and some new results in avoidance control, in "Proceedings of the 15th International Workshop on Dynamics and Control," Tossa de Mar, Spain, (2009), 166173. 
[39] 
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multiplayer pursuitevasion games, International Game Theory Review, 12 (2010), 117. doi: 10.1142/S0219198910002489. 
[40] 
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multiobjective problems, Applied Mathematics & Optimization, 66 (2012), 455473. 
[41] 
D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multiobjective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487493. 
[42] 
D. M. Stipanović, C. J. Tomlin and C. Valicka, Collision free coverage control with multiple agents, Proceedings of the RoMoCo'11 Conference, Bukowy Dworek, Poland, 2011. 
[43] 
E. M. Vaisbord and V. I. Zhukovskiy, "Introduction to MultiPlayer Differential Games and Their Applications," Gordon and Breach, New York, NY, 1988. 
[44] 
C. G. Valicka, S. R. Bieniawski, J. Vian, and D. M. Stipanović, Cooperative avoidance control for UAVs, Proceedings of the Tenth International Conference on Control, Automation, Robotics and Vision (ICARCV 2008), Hanoi, Vietnam (2008), 14621468. 
[45] 
T. L. Vincent and W. J. Grantham, "Nonlinear and Optimal Control Systems," John Wiley & Sons, Inc., New York, NY, 1997. 
[46] 
M. M. Zavlanos and G. J. Pappas, Potential fields for maintaining connectivity of mobile networks, IEEE Transactions on Robotics, 23 (2007), 812816. doi: 10.1109/TRO.2007.900642. 
[47] 
V. A. Zorich, "Mathematical Analysis II," SpringerVerlag, Berlin, Germany, 2004. 
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