A numerical approach for solving fractional optimal control problems using modified hat functions

被引:43
作者
Nemati, Somayeh [1 ,2 ]
Lima, Pedro M. [3 ]
Torres, Delfim F. M. [2 ]
机构
[1] Univ Mazandaran, Fac Math Sci, Dept Math, Babol Sar, Iran
[2] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat CIDMA, P-3810193 Aveiro, Portugal
[3] Univ Lisbon, Inst Super Tecn, Ctr Matemat Computac & Estocast, Ave Rovisco Pais, P-1049001 Lisbon, Portugal
来源
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 78卷
关键词
Fractional optimal control problems; Modified hat functions; Operational matrix of fractional integration; Inequality constraints; EQUATIONS;
D O I
10.1016/j.cnsns.2019.104849
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页数:14
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