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AN EFFICIENT NUMERICAL METHOD FOR SOLVING FRACTIONAL OPTIMAL CONTROL PROBLEMS WITH STATE AND CONTROL DELAYS | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 مرداد 1405 اصل مقاله (1.09 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70332.3487 | ||
| نویسندگان | ||
| Fahimeh Soltanian* ؛ Somayeh Montazerinezhad | ||
| Department of Mathematics, Payame Noor University,Tehran, Iran. | ||
| چکیده | ||
| The purpose of this paper is to introduce a numerical method for the solution of time-delay fractional optimal control problems (TDFOCPs) using the Chelyshkov wavelet and the Ritz spectral method. For the TDFOCP under consideration, two delay terms are presented in both the state and control functions. The dynamical system of the discussed TDFOCP consists of the fractional derivative in the Caputo sense. Initially, by employing the Chelyshkov wavelets through the Ritz method, the state function is approximated with unknown coefficients. Subsequently, the control function is computed by solving the Caputo fractional differential equation given in the constraint of the dynamical system. The next step involves substituting these approximations into the cost functional and utilizing the necessary optimality conditions. As a result, the TDFOCP becomes a problem of unconstrained optimization problem. Ultimately, the convergence analysis of the proposed method is investigated and five examples have been solved. Furthermore, the obtained results by the presented technique are compared with previous findings in the some existing literature to illustrate the effectiveness, validity and accuracy of the current approach. | ||
| کلیدواژهها | ||
| Fractional optimal control problems with time-delay؛ Ritz method؛ Chelyshkov wavelets؛ Riemann-Liouville fractional integration؛ Caputo fractional derivative | ||
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