On the numerical solution of optimal control problems via Bell polynomials basis

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 10، شماره 2 - شماره پیاپی 18، پاییز 2020، صفحه 197-221  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v10i2.86884

نویسندگان

Mohammad Reza Dadashi ¹؛ Ahmad Reza Haghighi²؛ Fahimeh Soltanian ¹؛ Ayatollah Yari¹

¹Department of Mathematics, Payame Noor University, Tehran, Iran.

²Department of Mathematics, Technical and Vocational University, Tehran, Iran.

چکیده

We present a new numerical approach to solve the optimal control problems (OCPs) with a quadratic performance index. Our method is based on the Bell polynomials basis. The properties of Bell polynomials are explained. We also introduce the operational matrix of derivative for Bell polynomials. The chief feature of this matrix is reducing the OCPs to an optimization problem. Finally, we discuss the convergence of the new technique and present some illustrative examples to show the effectiveness and applicability of the proposed scheme. Comparison of the proposed method with other previous methods shows that this method is accurate.

کلیدواژه‌ها

Optimal control problems؛ Bell polynomial؛ Best approximation؛ Operational matrix of derivative

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