A numerical treatment based on Bernoulli Tau method for computing the open-loop Nash equilibrium in nonlinear differential games

Mojteba Dehghan Banadaki | Hamid Navidi Ghaziani

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=169846
Date :  2022/10/01
Publish in :    Iranian Journal of Numerical Analysis and Optimization
DOI :  https://doi.org/10.22067/IJNAO.2022.74347.1086.
Link :  https://ijnao.um.ac.ir/article_41998.html
Keywords :Nonlinear differential games; Open-loop Nash equilibrium; Pontryagin’s maximum principle; Bernoulli Tau method.

Abstract :

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The Tau method based on the Bernoulli polynomials is implemented effciently to approximate the Nash equilibrium of open-loop kind in nonlinear differential games over a finite time horizon. By this treatment, the system of two-point boundary value problems of differential game extracted from Pontryagin’s maximum principle is transferred to a system of algebraic equations that Newton’s iteration method can be used for solving it. Also, for the mentioned approximation by the Bernoulli polynomials, the convergence analysis and the error upper bound are discussed. To demonstrate the applicably and accuracy of the proposed approach, some illustrated examples are presented at the final