Comparison of Dynamic Games in Application to Safe Ship Control

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The paper introduces methods of dynamic games for automation of ship control in the collision situation, the game control processes in marine navigation and the fundamental mathematical model of the game ship control. First, state equations, control and state constraints and then control goal function in the form of payments: the integral payment and the final one, have been defined. Multi-stage positional, and multi-step matrix, non-cooperative and cooperative, game and optimum control algorithms for a collision situation, have been presented. Te considerations have been illustrated with an exemplary computer simulation of algorithms to determine a safe own ship's trajectory in the process of passing the ships encountered in Kattegat Strait.

1. Basar T., Olsder G.J.: Dynamic noncooperative game theory. Siam, Philadelphia, 2013.

2. Baba N. and Jain L.C.: Computational intelligence in games. Physica-Verlag, New York, 2001.

3. Bist D.S.: Safety and security at sea. Butterworth Heinemann, Oxford-New Delhi, 2000.

4. Bole A., Dineley B., Wall A.: Radar and ARPA manual. Elsevier, Amsterdam-Tokyo, 2006.

5. Cahill R.A.: Collisions and their causes. Te Nautical Institute, London, 2002.

6. Cockcrof A.N., Lameijer N.F.: Collision avoidance rules. Elsevier, Amsterdam-Tokyo, 2006.

7. Engwerda J.C.: LQ dynamic optimization and diferential games. John Wiley and Sons, West Sussex, 2005.

8. Gluver H., Olsen D.: Ship collision analysis. Balkema, Rotterdam, 1998.

9. Isaacs R.: Diferential games. John Wiley and Sons, New York, 1965.

10. Millington I. and Funge J.: Artifcial intelligence for games. Elsevier, Amsterdam-Tokyo, 2009.

11. Modarres M.: Risk analysis in engineering. Taylor and Francis Group, Boca Raton, 2006.

12. Nisan N., Roughgarden T., Tardos E., Vazirani V.V.: Algorithmic game theory. Cambridge University Press, New York, 2007, p. 717-733.

13. Nise N.S.: Control systems engineering. John Wiley and Sons, New York, 2011.

14. Nowak A.S, Szajowski K.: Advances in dynamic games, applications to economics, fnance, optimization and stochastic control. Birkhauser, Boston, Basel, Berlin, 2000.

15. Osborne M.J.: An introduction to game theory. Oxford University Press, New York, 2004.

16. Pietrzykowski Z.: Te navigational decision support system on a sea-going vessel. Maritime University, Szczecin, 2011.

17. Radzik T.: Characterization of optimal strategies in matrix games with convexity properties. Game Teory, Vol. 29, No 2, 2000, p. 211-228.

18. Straffin P.D.: Game theory and strategy. Scholar, Warszawa, 2001 (in Polish).

19. Szłapczynski R., Śmierzchalski R.: Supporting navigators decisions by visualizing ship collision risk. Polish Maritime Research, Vol. 59, No 1, 2009, p. 83-88.

20. Zio E.: Computational methods for reliability and risk analysis. Quality, Reliability and Engineering Statistics, No 14, Word Scientifc, New Jersey-Chennai, 2009, p. 295-334.

Polish Maritime Research

The Journal of Gdansk University of Technology

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IMPACT FACTOR 2018: 1,214
5-year IMPACT FACTOR: 1,086

CiteScore 2018: 1.48

SCImago Journal Rank (SJR) 2018: 0.391
Source Normalized Impact per Paper (SNIP) 2018: 1.141

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