Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model

Mikulski, Leszek; Kropiowska, Dorota

doi:10.4467/2353737XCT.18.135.8974

Abstract

This article presents the usage of a zero-sum differential game to control a nonlinear object, which, in the analysed problem, was a mathematical pendulum. The obtained control was optimal with regard to adopted quality indicator for the worst interference. The two-point boundary value problem was solved numerically by means of the Dircol software application. Numerical solutions, meeting all the necessary optimality conditions, were obtained for different values of the rough parameter and for different values of damping.

References

[1] Basar T., Olsder G.J., Dynamic Noncooperative Game Theory, Academic Press, London/New York, 1995.
Search in Google Scholar Back to article
[2] Breitner M.H., Robust optimale Rückkopplungssteuerungen gegen unvorhersehbare Einflüsse: Differentialspielansatz, numerische Berechnung und Echtzeitapproximation, Reihe 8: Mess, Steuerung und Regelungstechnik, VDI Verlag, Düsseldorf, 1996.
Search in Google Scholar Back to article
[3] Breitner M.H., Pesch H.J., Grimm W., Complex Differential Games of Pursuit-Evasion Type with State Constraints, Part 1: Necessary Conditions for Optimal Open-Loop Strategies, Journal of Optimization Theory and Applications, Vol. 78, No. 3, 1993, 419–441.10.1007/BF00939876
Search in Google Scholar Back to article
[4] Butz T., von Stryk O., Modelling and Simulation of Electro- and Magnetorheological Fluid Dampers, ZAMM, Vol. 82, No. 1, 2002, 3–20.10.1002/1521-4001(200201)82:1<3::AID-ZAMM3>3.0.CO;2-O
Search in Google Scholar Back to article
[5] Hendzel Z., Penar P., Zastosowanie dwuosobowej gry różniczkowej o sumie zerowej do sterowania elementem mechatronicznym, Modelowanie Inżynierskie No. 60, 2016, 21–27.
Search in Google Scholar Back to article
[6] Pesch H.J., A Practical Guide to the Solution of Real-Life Optimal Control Problems, Control and Cybernetics, 23, 1/2, 1994, 7–60.
Search in Google Scholar Back to article
[7] Rettig U., von Stryk O., Optimal and Robust Damping Control for Semi-Active Vehicle Suspension, Progress in Industrial Mathematics at ECMI 2002, book series MATHINDUSTRY, Vol. 5, 2002, 353–361.10.1007/978-3-662-09510-2_48
Search in Google Scholar Back to article
[8] Starr A.W., Ho Y.C., Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 3, 1969, 184–206.10.1007/BF00929443
Search in Google Scholar Back to article
[9] von Stryk O., User’s guide for Dircol (Version 2.1): a direct collocation method for the numerical solution of optimal control problems, Technical report, Simulation and Systems Optimization Group, TU Darmstadt, 2002.
Search in Google Scholar Back to article
[10] Willems J.C., Dissipative Dynamical Systems, Part I: General Theory, Archive for Rational Mechanics and Analysis, Vol. 45, 1972, 321–351.10.1007/BF00276493
Search in Google Scholar Back to article

Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model

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