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Solving Fractional Optimal Control-Affine Problems via Fractional-Order Hybrid Jacobi Functions | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 8، دوره 9، شماره 1، مرداد 2024، صفحه 149-168 اصل مقاله (901.93 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2023.68826.1243 | ||
| نویسندگان | ||
| Zeinab Barary؛ AllahBakhsh Yazdani Cherati* ؛ Somayeh Nemati | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. | ||
| چکیده | ||
| This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and Jacobi polynomials. First, the corresponding Riemann-Liouville fractional integral operator of the introduced basis functions is calculated. Then, an approximation of the fractional derivative of the unknown state function is obtained by considering an approximation in terms of these basis functions. Next, using the dynamical system and applying the fractional integral operator, an approximation of the unknown control function is obtained based on the given approximations of the state function and its derivatives. Subsequently, all the given approximations are substituted into the performance index. Finally, the optimality conditions transform the problem into a system of algebraic equations. An error upper bound of the approximation of a function based on the fractional hybrid functions is provided. The method is applied to several numerical examples, and the experimental results confirm the efficiency and capability of the method. Furthermore, they demonstrate a good agreement between the approximate and exact solutions. | ||
| کلیدواژه‌ها | ||
| Fractional optimal control-affine problems؛ Fractional-order hybrid functions؛ Caputo derivative؛ Riemann-Liouville integral | ||
| مراجع | ||
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