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

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Dehghan Banadaki M.; Navidi H.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2022 | Volume:12 | Issue:2 Page(s): 467-482

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Title

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

Author(s)

Dehghan Banadaki M. | Navidi H. | Issue Writer Certificate

Keywords

Nonlinear differential gamesQ4

Open-loop Nash equilibriumQ4

Pon-tryagin’s maximum principleQ4

Bernoulli Tau methodQ4

Abstract

The Tau method based on the Bernoulli polynomials is implemented eﬀiciently to approximate the Nash equilibrium of open-loop kind in non-linear differential games over a finite time horizon. By this treatment, the system of two-point boundary value problems of differential game ex-tracted 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.

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