Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem

چکیده مقاله

In this paper, a novel framework is proposed for the solution of a general class of nonlinear two-dimensional optimal control problem (2DOCP), governed by Volterra singular partial integro-differential equation and a quadratic performance index. To this end, by the attributes of the bivariate Bernoulli polynomials, 2DOCP transmitted to a nonlinear programming (NLP) problem. For improving applicability, the operational matrix of two-dimensional singular integration is derived for the first time. Furthermore, we discuss comprehensively convergence analysis of the theoretical results. Numerical results are disclosed, to experimentally demonstrate the feasibility of the presented approach. © 2022, The Author(s), under exclusive licence to Islamic Azad University.