Application of optimization algorithm to nonlinear fractional optimal control problems

Journal of Computer & Robotics

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آذر 1402

نوع مقاله: Original Research (Full Papers)

شناسه دیجیتال (DOI): 10.22094/jcr.2023.1996770.1317

نویسندگان

Asma Moradikashkooli¹؛ Hamid Haj Seyyed Javadi^{* 2}؛ Sam Jabbehdari¹

¹Department of Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

²Department of Computer Engineering, Shahed University, Tehran, Iran

چکیده

In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivatives of GLPs is constructed. The operational matrices of the Caputo and ordinary derivatives are introduced. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method.

کلیدواژه‌ها

Generalized Laguerre polynomials؛ Nonlinear fractional optimal control problems؛ Optimization algorithm؛ Operational matrix؛ Coefficients and parameters