Abstract
Zero-sum differential game is a combination optimum control method and solution \( H_{\infty } \) control problem. Its solutions are based on Bellman’s principle of optimality, for which the solution for nonlinear dynamic object is not available. In this case, approximation method based on actor-critic algorithms are used. One of the approximation method – SPIA [1] was applied in wheeled mobile robot tracking control problem and presented in the article. Numerical tests for the solution of the zero-sum differential game approximating algorithm were compared with the classical PD algorithm.
The obtained results confirm theoretical assumptions concerning the relationship between zero-sum differential game and \( H_{\infty } \) control problem.
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References
Vamvoudakis, K.G., Lewis, F.L.: Online solution of nonlinear two-player zero-sum games using synchronous policy iteration. Int. J. Robust Nonlinear Control 22, 1460–1483 (2012)
Vamvoudakis, K.G., Lewis, F.L.: Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5), 878–888 (2010)
Zhu, Y., et al.: Iterative adaptive dynamic programming for solving unknown nonlinear zero-sum game based on online data, pp. 1–12 (2016)
Van der Schaft, A.J.: L2-gain analysis of nonlinear systems and nonlinear state feedback H-infinity Control. IEEE Trans. Autom. Control 37(6), 770–784 (1992)
Abu-Khalaf, M., et al.: Nonlinear H2/H-Infinity Constrained Feedback Control. Springer, London (2006)
Starr, A.W., Ho, Y.C.: Nonzero-sum differential games. J. Optim. Theory Appl. 3(3), 184–206 (1969)
Wang, F.-Y., Zhang, H., Liu, D.: Adaptive dynamic programming: an introduction. IEEE Comput. Intell. Mag. 4(May), 39–47 (2009)
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. The MIT Press, Cambridge (1998)
Yasini, S., et al.: Online concurrent reinforcement learning algorithm to solve two-player zero-sum games for partially unknown nonlinear continuous-time systems. Int. J. Adapt. Control Signal Process. 22(4), 325–343 (2008)
Żylski, W.: Kinematic and Dynamic of a Wheeled Mobile Robot (in Polish). Rzeszow University of Technology, Rzeszow (1996)
Gierlak, P., Hendzel, Z.: Control of a Wheel and Manipulation Robot (in Polish) (2011)
Brogliato, B., et al.: Dissipative Systems Analysis and Control. Springer, London (2007)
Wang, D., et al.: Event-based input-constrained nonlinear H-infinity state feedback with adaptive critic and neural implementation. Neurocomputing 214, 848–856 (2016)
Yasini, S., et al.: Approximate dynamic programming for two-player zero-sum game related to H-infinity control of unknown nonlinear continuous-time systems. Int. J. Control Autom. Syst. 13(1), 99–109 (2014)
Hendzel, Z., Penar, P.: Application of differential games in mechatronic control system. Int. J. Appl. Mech. Eng. 21(4), 867–878 (2016)
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Hendzel, Z., Penar, P. (2019). Zero-Sum Differential Game in Wheeled Mobile Robot Control. In: Świder, J., Kciuk, S., Trojnacki, M. (eds) Mechatronics 2017 - Ideas for Industrial Applications. MECHATRONICS 2017. Advances in Intelligent Systems and Computing, vol 934. Springer, Cham. https://doi.org/10.1007/978-3-030-15857-6_16
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DOI: https://doi.org/10.1007/978-3-030-15857-6_16
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