Approximate Solutions for a Certain Class of Fractional Optimal Control Problems Using Laguerre Collocation Method
نویسندگان
چکیده
In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Laguerre polynomials approximation and Rayleigh-Ritz method are used to reduce FOCPs to solve a system of algebraic equations which solved using Newton iteration method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method. Mathematics Subject Classification: 65N20, 41A30
منابع مشابه
A 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 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 کاملA Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions
In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, the unknown functions are approximated by the hybrid functions, including Bernoulli polynomials and Block-pulse functions based o...
متن کاملAn iterative scheme for a class of fractional optimal control problems
This paper presents a hybrid scheme based on Dinkelbach approach and wavelet collocation method to extract approximate solutions of fractional optimal control problems (FOCP)’s. First Dinkelbach approach is considered to linearize the problem, then it is tried by combination of collocation wavelet approach and a numerical scheme of solving nonlinear equations, an iterative approach be proposed ...
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 کامل