AUTHOR(S): Ivan G. Ivanov, Nikolay Netov, Vladislav Tanov
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TITLE Iteratively Computation the Nash Equilibrium Points in the Two-Player Positive Games |
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ABSTRACT We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The accelerated Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in [6], where the convergence properties are established. In addition, the Lyapunov iterative method to compute the Nash equilibrium point is presented in [7] (5th International Conference Applied and Computational Mathematics, WSEAS Conference at Mallorca, 2016). Based on these two methods we derive a new one - the accelerated Lyapunov method. Moreover, the convergence properties are proved. The performances of the proposed algorithm are illustrated on some numerical examples. |
KEYWORDS feedback Nash equilibrium, generalized Riccati equation, stabilizing solution, nonnegative solution |
REFERENCES [1] T. Azevedo-Perdicoulis and G. Jank, Linear Quadratic Nash Games on Positive Linear Systems, European Journal of Control, 11, 2005, 1– 13. [1] T. Azevedo-Perdicoulis and G. Jank, Linear Quadratic Nash Games on Positive Linear Systems, European Journal of Control, 11, 2005, 1– 13. |
Cite this paper Ivan G. Ivanov, Nikolay Netov, Vladislav Tanov. (2016) Iteratively Computation the Nash Equilibrium Points in the Two-Player Positive Games. International Journal of Mathematical and Computational Methods, 1, 378-381 |
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