A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation

Author(s):

Mojtaba Dehghan Banadaki , Hamidreza Navidi *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In the present study, an efficient combination of the Tau method with the Bernoulli polynomials is proposed for computing the Feedback Nash equilibrium in differential games over a finite horizon. By this approach, the system of Hamilton-Jacobi Bellman equations of a differential game derived from Bellman’s optimality principle is transferred to a nonlinear system of algebraic equations solvable by using Newton’s iteration method. Some illustrative examples are provided to show the accuracy and efficiency of the proposed numerical method.
Keywords:

Differential games , Feedback Nash equilibrium , Bellman’s optimality principle , Bernoulli Tau method

Language:
English
Published:
Computational Methods for Differential Equations, Volume:10 Issue: 4, Autumn 2022
Pages:
894 to 904
https://www.magiran.com/p2492001  
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