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Orbital transfers: optimization methods and recent results
A note on monotone approximations of minimum and maximum functions and multi-objective problems
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. | College of Engineering, University of California at Berkeley, Berkeley, California, United States |
This note presents a preview of the treatment in [12].
References:
[1] |
A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2nd edition, Springer-Verlag, Berlin, Germany, 2005. |
[2] |
R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996. |
[3] |
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975. |
[4] |
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591.
doi: 10.1007/BF00933298. |
[5] |
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576.
doi: 10.1007/BF00934040. |
[6] |
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342.
doi: 10.1002/oca.4660040406. |
[7] |
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1999.
doi: 10.1007/978-1-4615-5563-6. |
[8] |
D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multi-player pursuit-evasion games, in "Proceedings of the Eleventh International Symposium on Dynamic Games and Applications," Tucson, Arizona, 2004. |
[9] |
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. |
[10] |
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. |
[11] |
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. |
[12] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Submitted to Applied Mathematics & Optimization. |
show all references
References:
[1] |
A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2nd edition, Springer-Verlag, Berlin, Germany, 2005. |
[2] |
R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996. |
[3] |
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975. |
[4] |
G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591.
doi: 10.1007/BF00933298. |
[5] |
G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576.
doi: 10.1007/BF00934040. |
[6] |
G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342.
doi: 10.1002/oca.4660040406. |
[7] |
K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1999.
doi: 10.1007/978-1-4615-5563-6. |
[8] |
D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multi-player pursuit-evasion games, in "Proceedings of the Eleventh International Symposium on Dynamic Games and Applications," Tucson, Arizona, 2004. |
[9] |
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. |
[10] |
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. |
[11] |
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. |
[12] |
D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Submitted to Applied Mathematics & Optimization. |
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