DOAJ Open Access 2022

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

M. Dehghan Banadaki H. Navidi

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Applied mathematics. Quantitative methods

Penulis (2)

M. Dehghan Banadaki

H. Navidi

Format Sitasi

APA MLA BibTeX

Banadaki, M.D., Navidi, H. (2022). A numerical treatment based on Bernoulli Tau method for computing the open-loop Nash equilibrium in nonlinear differential games. https://doi.org/10.22067/ijnao.2022.74347.1086

Akses Cepat

Lihat di Sumber doi.org/10.22067/ijnao.2022.74347.1086

Informasi Jurnal

Tahun Terbit: 2022
Sumber Database: DOAJ
DOI: 10.22067/ijnao.2022.74347.1086
Akses: Open Access ✓