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A numerical technique for solving fractional optimal control problems. (English) Zbl 1228.65109
Summary: We present a numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. The method is based upon the Legendre orthonormal polynomial basis. The operational matrices of fractional Riemann-Liouville integration and multiplication, along with the Lagrange multiplier method for the constrained extremum are considered. By this method, the given optimization problem reduces to the problem of solving a system of algebraic equations. By solving this system, we achieve the solution of the FOCP. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

65L05 Numerical methods for initial value problems
49M30 Other numerical methods in calculus of variations (MSC2010)
34A08 Fractional ordinary differential equations and fractional differential inclusions
26A33 Fractional derivatives and integrals
45J05 Integro-ordinary differential equations
49K21 Optimality conditions for problems involving relations other than differential equations
Full Text: DOI
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