Multi-criteria multi-stage game optimization

• Autorzy: Lisowski Józef

Identyfikatory

DOI

10.24136/jaeee.2022.005

Warianty tytułu

PL

Wielokryterialna optymalizacja gry wieloetapowej

• Języki publikacji: EN

Abstrakty

EN

The article presents a mathematical model of a multi-stage game of the process of safe control of a transport object in possible collision situations with other encountered objects, containing a description of state variables, state and control constraints, and sets of permissible object strategies. Multi-criteria optimization tasks were formulated in the form of positional and matrix games under the conditions of playing non-cooperative and cooperative control as well as non-game optimal control. The multi-criteria control algorithms corresponding to these tasks were computer simulated in Matlab / Simulink on the example of a real situation.

PL

W artykule przedstawiono model matematyczny wieloetapowej gry procesu bezpiecznego sterowania obiektem transportowym w możliwych sytuacjach kolizyjnych z innymi spotkanymi obiektami, zawierający opis zmiennych stanu, ograniczeń stanu i sterowania oraz zbiory dopuszczalnych strategii obiektów. Sformułowano wielokryterialne zadania optymalizacyjne w postaci gry pozycyjnej i macierzowej, w warunkach rozgrywającego sterowania niekooperacyjnego i kooperacyjnego oraz nierozgrywającego sterowania optymalnego. Algorytmy sterowania wielokryterialnego odpowiadające tym zadaniom poddano symulacji komputerowej w programie Matlab/Simulink na przykładzie rzeczywistej sytuacji.

Słowa kluczowe

EN

optimization; control engineering; game theory; computer simulation

PL

optymalizacja; automatyka; teoria gier; symulacja komputerowa

• Wydawca: Uniwersytet Technologiczno-Humanistyczny im. Kazimierza Pułaskiego w Radomiu
• Czasopismo: Journal of Automation, Electronics and Electrical Engineering
• Rocznik: 2022
• Tom: Vol. 4, No. 1
• Strony: 37--42
• Opis fizyczny: Bibliogr. 31 poz., rys., wykr.

Twórcy

autor

Lisowski Józef

• Gdynia Maritime University, Faculty of Electrical Engineering, Poland

Bibliografia

• 1. Baker G. (2016) Differential Equations as Models in Science and Engineering. World Scientific, New Jersey.
• 2. Basar T.; Olsder G.J. (2013) Dynamic Non-Cooperative Game Theory. Siam, Philadelphia, ISBN: 978-0-898-714- 29-6.
• 3. Chen Y., Georgiou T.T., Pavon M. (2019) Covariance steering in zero-sum linear-quadratic two-player differential games. arXiv, arXiv: 1909.05468v1.
• 4. Dorf R.C., Bishop R.H. (2012) Modern control systems. Addison Wesley Longman, California.
• 5. Ehrgott M., Gandibleux X. 2002. Multiple criteria optimization: state of the art annotated bibliographic surveys. Kluwer Academic Press, New York.
• 6. Engwerda, J.C. (2005) LQ Dynamic optimization and differential games. John Wiley & Sons, New Jork, ISBN: 978-0-470-01524-7.
• 7. Falcone M., Ferretti R. (2014) Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations. Sian, Philadelphia.
• 8. Gronbaek L., Lindroos M., Munro G., Pintassilgo P. (2020) Cooperative Games in Fisheries with More than Two Players. In Game Theory and Fisheries Management; Springer: Cham, Switzerland, 81–105, ISBN: 978-3-030- 40112-2.
• 9. Guenin B., Konemann J., Tuncel L. (2014) A gentle introduction to optimization. Cambridge University Press, United Kingdom.
• 10. Hermes H., Isaacs R. (1965) Differential Games. Math. Comput., vol. 19, 700, doi: 10.2307/2003985.
• 11. Hosseinzadeh M., Garone E., Schenato L. (2018) A Distributed Method for Linear Programming Problems with Box Constraints and Time-Varying Inequalities. IEEE Control. Syst. Lett., vol. 3, 404–409, doi: 10.1109/lcsys.2018.2889963.
• 12. Isaacs R. (1965) Differential Games. John Wiley & Sons, New York, ISBN: 0-48640-682-2.
• 13. Kim I.Y., de Weck O.L. (2005) Adaptive weighted sum method for bi-objective optimization: Pareto front generation”. Structural Multidisciplinary Optimization. vol 29, issue 2, 149-158, doi: 10.1007/s00158-004-0465- 1.
• 14. Koksalan M., Wallenius J., Zionts S. (2013) Early history of multiple criteria decision making. Journal of Multic Criteria Decision Analysis. vol 20, 87-94, doi: 10.1002/mcda.1481.
• 15. Lazarowska A. (2022) Safe trajectory planning for maritime surface ships. Springer Series on Naval Architecture, Marine Engineering, Shipbuilding and Shipping, vol. 13, 1-185, doi: 10.1007/978-3-030-97715- 3.
• 16. Legriel J. (2011) Multicriteria optimization and its application to multi-processor embedded systems. A thesis of doctorate, Grenoble University, France.
• 17. Li Y., Vorobeychik, Y. (2019) Path planning games. Multiagent Syst., arXiv, arXiv:1910.13880.
• 18. Lisowski J. (2022) Optimization methods (in Polish). Publishing House of Gdynia Maritime University, Gdynia, ISBN: e-book 978-83-7421-408-7.
• 19. Liu Z., Wu Z., Zheng Z. (2019) A cooperative game approach for assessing the collision risk in multi-vessel encountering. Ocean Eng., 106175, doi: 10.1016/j.oceaneng.2019.106175.
• 20. Marler R.T., Arora J.S. (2004) Survey of multi-objective optimization methods for engineering. Structural Multidisciplinary Optimization. vol 26, 369-395, doi: 10.1007/s00158-003-0368-6.
• 21. Messac A., Mattson C.A. (2002) Generating well distributed sets of Pareto points for engineering design using physical programming. Journal of Optimization Eng., vol 3, 431-450, doi: 10.1023/A:1021179727569.
• 22. Messac A., Sukam C.P., Melachrinoudis E. (2000) Aggregate objective functions and Pareto frontiers: required relationships and practical implications. Journal of Optimization Eng., vol 1, 171-188, doi: 10.1023/A:1010035730904.
• 23. Millington I., Funge J. (2018) Artificial Intelligence for Games. CRC Press, Boca Raton.
• 24. Nicotra M.M., Liao-McPherson D., Kolmanovsky I.V. Embedding Constrained Model Predictive Control in a Continuous-Time Dynamic Feedback. IEEE Trans. Autom. Control, vol 64, 1932–1946, doi: 10.1109/tac.2018.2867359.
• 25. Nisan N., Roughgarden T., Tardos E., Vazirani V.V. (2007) Algorithmic game theory. Cambridge University Press, New York.
• 26. Odu G.O., Charles-Owaba O.E. (2013) Review of multi criteria optimization methods – theory and applications. IOSR J of Eng., vol 3, No 10, 01-14, doi: 10.9790/3021- 031020114.
• 27. Osborne M.J. An (2004) Introduction to Game Theory. Oxford University Press, New York, ISBN: 978-0-19- 512895-6.
• 28. Speyer J.L., Jacobson D.H. (2010) Primer on optimal control theory. SIAM, Toronto.
• 29. Spica R., Cristofalo E., Wang Z., Montijano E., Schwager M. (2020) A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing. IEEE Trans. Robot., vol. 36, 1389–1403, doi: 10.1109/tro.2020.2994881.
• 30. Wells D. (2003) Game and Mathematics. Cambridge University Press, London, ISBN 978-1-78326-752-1.
• 31. Yong J. (2018) Optimization Theory – a Concise Introduction. World Scientific, New Jersey