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An Efficient Numerical Solution of Fractional Optimal Control Problems by using the Ritz Method and Bernstein Operational Matrix
Author(s) -
Nemati Ali,
Yousefi Sohrabali,
Soltanian Fahimeh,
Ardabili J.Saffar
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1321
Subject(s) - ritz method , mathematics , algebraic equation , convergence (economics) , mathematical optimization , optimal control , matrix (chemical analysis) , fractional calculus , boundary value problem , mathematical analysis , nonlinear system , physics , materials science , quantum mechanics , economics , composite material , economic growth
This paper deals with the Ritz spectral method to solve a class of fractional optimal control problems (FOCPs). The developed numerical procedure is based on the function approximation by the Bernstein polynomials along with fractional operational matrix usage. The approximation method is computationally consistent and moreover, has a good flexibility in the sense of satisfying the initial and boundary conditions of the optimal control problems. We construct a new fractional operational matrix applicable in the Ritz method to estimate the fractional and integer order derivatives of the basis. As a result, we achieve an unconstrained optimization problem. Next, by applying the necessary conditions of optimality, a system of algebraic equations is obtained. The resultant problem is solved via Newton's iterative method. Finally, the convergence of the proposed method is investigated and several illustrative examples are added to demonstrate the effectiveness of the new methodology.