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Jamming in mobile networks: A game-theoretic approach
Safe and reliable coverage control
1. | Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, 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," 2ndedition, Springer-Verlag, 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), 89-97.
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), 44-63. |
[4] |
F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 3-12. |
[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), 3713-3718.
doi: 10.1109/ACC.2008.4587071. |
[6] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," Mc-Graw 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), 1-11.
doi: 10.1016/0898-1221(87)90090-3. |
[8] |
M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161-170.
doi: 10.1016/0898-1221(89)90133-8. |
[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), 615-627.
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," Springer-Verlag, 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), 2040-2055.
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), 642-657.
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), 3420-3425.
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," Orion-Art, Belgrade, Serbia, 2005. |
[22] |
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591.
doi: 10.1007/BF00933298. |
[23] |
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576.
doi: 10.1007/BF00934040. |
[24] |
G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850-851.
doi: 10.1109/TAC.1980.1102408. |
[25] |
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342.
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 multi-agent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107-126.
doi: 10.1177/0278364907084441. |
[27] |
A. A. Melikyan, The problem of time-optimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 1-7. |
[28] |
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998.
doi: 10.1007/978-1-4615-5563-6. |
[29] |
I. Mitchell, A. M. Bayen and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947-957.
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. Rodríguez-Seda, 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), 984-992.
doi: 10.1109/TCST.2009.2030176. |
[32] |
E. J. Rodríguez-Seda, 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 car-like robots on a receding horizon, Proceedings of the 2009 IEEE Multi-conference 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 multi-player pursuit-evasion 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 multi-agent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699-707.
doi: 10.1115/1.2764510. |
[37] |
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multi-player pursuit-evasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133-145. |
[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), 166-173. |
[39] |
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multi-player pursuit-evasion games, International Game Theory Review, 12 (2010), 1-17.
doi: 10.1142/S0219198910002489. |
[40] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Applied Mathematics & Optimization, 66 (2012), 455-473. |
[41] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multi-objective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487-493. |
[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 Multi-Player 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), 1462-1468. |
[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), 812-816.
doi: 10.1109/TRO.2007.900642. |
[47] |
V. A. Zorich, "Mathematical Analysis II," Springer-Verlag, Berlin, Germany, 2004. |
show all references
References:
[1] |
A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2ndedition, Springer-Verlag, 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), 89-97.
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), 44-63. |
[4] |
F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 3-12. |
[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), 3713-3718.
doi: 10.1109/ACC.2008.4587071. |
[6] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," Mc-Graw 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), 1-11.
doi: 10.1016/0898-1221(87)90090-3. |
[8] |
M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161-170.
doi: 10.1016/0898-1221(89)90133-8. |
[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), 615-627.
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," Springer-Verlag, 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), 2040-2055.
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), 642-657.
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), 3420-3425.
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," Orion-Art, Belgrade, Serbia, 2005. |
[22] |
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591.
doi: 10.1007/BF00933298. |
[23] |
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576.
doi: 10.1007/BF00934040. |
[24] |
G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850-851.
doi: 10.1109/TAC.1980.1102408. |
[25] |
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342.
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 multi-agent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107-126.
doi: 10.1177/0278364907084441. |
[27] |
A. A. Melikyan, The problem of time-optimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 1-7. |
[28] |
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998.
doi: 10.1007/978-1-4615-5563-6. |
[29] |
I. Mitchell, A. M. Bayen and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947-957.
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. Rodríguez-Seda, 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), 984-992.
doi: 10.1109/TCST.2009.2030176. |
[32] |
E. J. Rodríguez-Seda, 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 car-like robots on a receding horizon, Proceedings of the 2009 IEEE Multi-conference 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 multi-player pursuit-evasion 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 multi-agent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699-707.
doi: 10.1115/1.2764510. |
[37] |
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multi-player pursuit-evasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133-145. |
[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), 166-173. |
[39] |
D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multi-player pursuit-evasion games, International Game Theory Review, 12 (2010), 1-17.
doi: 10.1142/S0219198910002489. |
[40] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Applied Mathematics & Optimization, 66 (2012), 455-473. |
[41] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multi-objective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487-493. |
[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 Multi-Player 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), 1462-1468. |
[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), 812-816.
doi: 10.1109/TRO.2007.900642. |
[47] |
V. A. Zorich, "Mathematical Analysis II," Springer-Verlag, Berlin, Germany, 2004. |
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