Numerical solution of a class of two-dimensional quadratic optimal control problems by using Ritz method

2015 ◽  
Vol 37 (4) ◽  
pp. 765-781 ◽  
Author(s):  
Kamal Mamehrashi ◽  
Sohrab Ali Yousefi
Keyword(s):  
Optimal Control ◽  
Numerical Solution ◽  
Optimal Control Problems ◽  
Ritz Method ◽  
Control Problems ◽  
Two Dimensional ◽  
Quadratic Optimal Control

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 new operational matrix based on Boubaker wavelet for solving optimal control problems of arbitrary order

2020 ◽  
Vol 42 (10) ◽  
pp. 1858-1870 ◽  
Author(s):  
Kobra Rabiei ◽  
Yadollah Ordokhani
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Arbitrary Order ◽  
Ritz Method ◽  
Operational Matrix ◽  
Similar Process ◽  
Control Problems ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
The One

This paper presents numerical solution for solving the nonlinear one and two-dimensional optimal control problems of arbitrary order. First, we have constructed Boubaker wavelet for the first time and defined a general formulation for its fractional derivative operational matrix. To solve the one-dimensional problem, we have transformed the problems into an optimization one. The similar process together with the Ritz method are applied to find a solution for two-dimensional problems as well. Then, the necessary conditions of optimality result in a system of algebraic equations with unknown coefficients and then control parameters can be simply solved. The error vector is considered to show the convergence of the used approximation in this method. Finally, some illustrative examples are given to demonstrate accuracy and efficiency of the proposed method.

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