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A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. (English) Zbl 1182.70047
The paper deals with a direct numerical technique for fractional optimal control problems (FOCPs). The FOCPs are formulated in terms of Riemann-Liouville fractional derivatives (RLFDs). It is demonstrated that the right RLFDs automatically arise in the formulation when the dynamics of the system is described using RLFDs only. For numerical computation, the fractional derivatives are approximated using their Grunwald-Letnikov definition. This leads to a set of algebraic equations that can be solved using numerical techniques. Two examples, one time-invariant and the other time-dependent, are considered to demonstrate the effectiveness of the formulation. Some details of the numerical scheme are discussed.
70Q05Control of mechanical systems (general mechanics)
70-08Computational methods (mechanics of particles and systems)
26A33Fractional derivatives and integrals (real functions)