An Efficient Numerical Solution of Fractional Optimal Control Problems by using the Ritz Method and Bernstein Operational Matrix

2016 ◽  
Vol 18 (6) ◽  
pp. 2272-2282 ◽  
Author(s):  
Ali Nemati ◽  
Sohrabali Yousefi ◽  
Fahimeh Soltanian ◽  
J.Saffar Ardabili
Keyword(s):  
Optimal Control ◽  
Numerical Solution ◽  
Optimal Control Problems ◽  
Ritz Method ◽  
Operational Matrix ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

scholarly journals Numerical Solution of Some Types of Fractional Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Tamer Mostafa Al-Ajami ◽  
Ronald H. W. Hoppe
Keyword(s):  
Optimal Control ◽  
Numerical Solution ◽  
Optimal Control Problems ◽  
Ritz Method ◽  
Necessary Optimality Conditions ◽  
State Equation ◽  
The State ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.

A Numerical Method for Solving Fractional Optimal Control Problems Using Ritz Method

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Ali Nemati ◽  
Sohrab Ali Yousefi
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimal Control Problems ◽  
Ritz Method ◽  
Operational Matrix ◽  
New Method ◽  
Control Problems ◽  
State Function ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

Our paper presents a new method to solve a class of fractional optimal control problems (FOCPs) based on the numerical polynomial approximation. In the proposed method, the fractional derivative in the dynamical system is considered in the Caputo sense. The approach used here is to approximate the state function by the Legendre orthonormal basis by using the Ritz method. Next, we apply a new constructed operational matrix to approximate fractional derivative of the basis. After transforming the problem into a system of algebraic equations, the problem is solved via the Newton's iterative method. Finally, the convergence of the new method is investigated and some examples are included to illustrate the effectiveness and applicability of the proposed methodology.

Study of B-spline collocation method for solving fractional optimal control problems

2021 ◽  
pp. 014233122098753
Author(s):  
Yousef Edrisi-Tabriz ◽  
Mehrdad Lakestani ◽  
Mohsen Razzaghi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Operational Matrix ◽  
Control Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
A Direct Method

In this article, a class of fractional optimal control problems (FOCPs) are solved using a direct method. We present a new operational matrix of the fractional derivative in the sense of Caputo based on the B-spline functions. Then we reduce the solution of fractional optimal control problem to a nonlinear programming (NLP) one, where some existing well-developed algorithms may be applied. Numerical results demonstrate the efficiency of the presented technique.

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