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- Title
Fractional-Order Legendre Functions and Their Application to Solve Fractional Optimal Control of Systems Described by Integro-differential Equations.
- Authors
Rabiei, Kobra; Ordokhani, Yadollah; Babolian, Esmaeil
- Abstract
In this paper, we introduce a set of functions called fractional-order Legendre functions (FLFs) to obtain the numerical solution of optimal control problems subject to the linear and nonlinear fractional integro-differential equations. We consider the properties of these functions to construct the operational matrix of the fractional integration. Also, we achieved a general formulation for operational matrix of multiplication of these functions to solve the nonlinear problems for the first time. Then by using these matrices the mentioned fractional optimal control problem is reduced to a system of algebraic equations. In fact the functions of the problem are approximated by fractional-order Legendre functions with unknown coefficients in the constraint equations, performance index and conditions. Thus, a fractional optimal control problem converts to an optimization problem, which can then be solved numerically. The convergence of the method is discussed and finally, some numerical examples are presented to show the efficiency and accuracy of the method.
- Subjects
LEGENDRE'S functions; INTEGRO-differential equations; OPTIMAL control theory; NUMERICAL solutions to integro-differential equations; NUMERICAL solutions to nonlinear difference equations; NUMERICAL solutions to linear differential equations; ALGEBRAIC equations
- Publication
Acta Applicandae Mathematicae, 2018, Vol 158, Issue 1, p87
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-018-0175-0