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ISSN 2083-6473
ISSN 2083-6481 (electronic version)
 

 

 

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Associate Editor
Tomasz Neumann
 

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TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
www http://www.transnav.eu
e-mail transnav@am.gdynia.pl
Multi-criteria Optimization of Multi-step Matrix Game in Collision Avoidance of Ships
1 Gdynia Maritime University, Gdynia, Poland
ABSTRACT: This research article formulates a mathematical model of the matrix game of the safe ship control process containing: state variables and control, collision risk definition and the form of a collision risk matrix. Multicriteria optimization of the matrix game was introduced, leading to non-cooperative and cooperative game control algorithms and non-game control. Simulation safe trajectories of own ship for various types of control were compared to the example of the real situation at sea.
REFERENCES
Basar, T. & Bernhard, P. 2008. H-Infinity optimal control and related mini-max design problems: A dynamic game approach. Berlin: Springer. - doi:10.1007/978-0-8176-4757-5
Bist, D.S. 2000. Safety and security at sea. Oxford-New Delhi: Butter Heinemann.
Breton, M., & Szajowski, K. 2010. Advances in dynamic games: theory, applications, and numerical methods for differential and stochastic games. Boston: Birkhauser. - doi:10.1007/978-0-8176-8089-3
Ehrgott, M. 2005. Multicriterial optimization. Berlin: Springer.
Ehrgott, M. & Gandibleux, X. 2002. Multiple criteria optimization: state of the art annotated bibliographic surveys. New York: Kluwer Academic Press. - doi:10.1007/b101915
Engwerda, J.C. 2005. LQ dynamic optimization and differential games. New York: John Wiley & Sons.
Eshenauer, H., Koski, J., Osyczka, A. 1990. Multicriteria design optimization: procedures and application. Berlin: Springer-Verlag. - doi:10.1007/978-3-642-48697-5
Isaacs, R. 1965. Differential games. New York: John Wiley & Sons.
Kazimierski, W. & Stateczny. A. 2013. Fusion of Data from AIS and Tracking Radar for the Needs of ECDIS, Proc. of the Signal Processing Symp., Jachranka, Poland. - doi:10.1109/SPS.2013.6623592
Kouemou, G. 2009. Radar technology. Chapter 4 by Józef Lisowski: Sensitivity of safe game ship control on base information from ARPA radar. Croatia, In-tech, 61-86.
Kun, G. 2001. Stabilizability, controllability, and optimal strategies of linear and nonlinear dynamical games. PhD. Thesis. Aachen: RWTH.
Lazarowska, A. 2017. A new deterministic approach in a decision support system for ship’s trajectory planning. Expert Systems with Applications, Vol. 71, Issue C: 469–478. - doi:10.1016/j.eswa.2016.11.005
Lisowski, J. 2014. Optimization-supported decision-making in the marine game environment. Solid State Phenomena, Vol. 210: 215-222. - doi:10.4028/www.scientific.net/SSP.210.215
Mesterton-Gibbons, M. 2001. An introduction to game theoretic modeling. Providence: American Mathematical Society. - doi:10.1090/stml/011
Millington, I. & Funge, J. 2009. Artificial intelligence for games. Amsterdam-Tokyo: Elsevier. - doi:10.1016/B978-0-12-374731-0.00008-6
Miloh, T. 1974. Determination of critical manoeuvres for collision avoidance using the theory of differential games. Hamburg: Inst. Fur Schiffbau.
Modarres, M. 2006. Risk analysis in engineering. Boca Raton: Taylor & Francis Group.
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. 2007. Algorithmic game theory. New York: Cambridge University Press. - doi:10.1017/CBO9780511800481
Olsder, G.J. & Walter, J.L. 1977. A differential game approach to collision avoidance of ships. Proc. of the 8th IFIP Symp. on Optimization Techniques, Novosibirsk, 264-271. - doi:10.1007/BFb0007243
Osborne, M.J. 2004. An introduction to game theory. New York: Oxford University Press.
Perez, T. 2005. Ship motion control. London: Springer.
Polak, E., Lee. S., Bustany, I., Madhan, A. 2016. Method of approximations and adaptive approximations for a class of matrix games. Journal of Optimization Theory and Applications, Vol. 170, No. 3: 876-899. - doi:10.1007/s10957-016-0953-7
Straffin, P.D. 2001. Game theory and strategy. Warszawa: Scholar.
Szlapczynski, R. & Szlapczynska, J. 2016. An analysis of domain-based ship collision risk parameters, Ocean Eng., Vol. 126: 47-56, - doi:10.1016/j.oceaneng.2016.08.030
Tomera, M. 2012. Nonlinear Observers Design for Multivariable Ship Motion Control, Polish Maritime Research, Vol. 19, Special Issue 1: 50-56 - doi:10.2478/v10012-012-0023-5
Xu, Q. & Wang, N. 2014. A survey on ship collision risk evaluation. Promet – Traffic & Transportation, Vol. 26, No. 6: 475-486. - doi:10.7307/ptt.v26i6.1386
Wells, D. 2013. Games and mathematics. Cambridge: Cambridge University Press.
Citation note:
Lisowski J.: Multi-criteria Optimization of Multi-step Matrix Game in Collision Avoidance of Ships. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 13, No. 1, doi:10.12716/1001.13.01.12, pp. 125-131, 2019

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