Numerical Method for Solving Fractional Optimal Control Problems
نویسندگان
چکیده
1 Professor and author of correspondence, Phone: +91 3222-283084, Fax: +91 3222 255303, Email: [email protected] ABSTRACT A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from the formulation. Examples considered here show that the numerical results obtained using this and other techniques agree very well.
منابع مشابه
A spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...
متن کاملNew operational matrix for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative
In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...
متن کاملBiorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...
متن کاملA Neural Network Method Based on Mittag-Leffler Function for Solving a Class of Fractional Optimal Control Problems
In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...
متن کاملNumerical Solution of Delay Fractional Optimal Control Problems using Modification of Hat Functions
In this paper, we consider the numerical solution of a class of delay fractional optimal control problems using modification of hat functions. First, we introduce the fractional calculus and modification of hat functions. Fractional integral is considered in the sense of Riemann-Liouville and fractional derivative is considered in the sense of Caputo. Then, operational matrix of fractional inte...
متن کاملA New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...
متن کامل