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

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Abstract

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.

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Acknowledgements

The first author would like to appreciate the research council of Farhangian University for supporting this research. The second author would like to thank the National Center for Medical Education Assessment for supporting this research work.

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Authors and Affiliations

  1. Department of Educational Mathematics, Farhangian University, Tehran, Iran

    Asiyeh Ebrahimzadeh

  2. National Center for Medical Education Assessment, Tehran, Iran

    Samaneh Panjeh Ali Beik

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  1. Asiyeh Ebrahimzadeh
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  2. Samaneh Panjeh Ali Beik
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Correspondence to Asiyeh Ebrahimzadeh.

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Ebrahimzadeh, A., Panjeh Ali Beik, S. Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem. Math Sci 17, 325–335 (2023). https://doi.org/10.1007/s40096-022-00473-1

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