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An approximate method for numerically solving fractional order optimal control problems of general form. (English) Zbl 1189.49045
Summary: We discuss fractional order optimal control problems (FOCPs) and their solutions by means of rational approximation. The methodology developed here allows us to solve a very large class of FOCPs (linear/nonlinear, time-invariant/time-variant, SISO/MIMO, state/input constrained, free terminal conditions etc.) by converting them into a general, rational form of optimal control problem (OCP). The fractional differentiation operator used in the FOCP is approximated using Oustaloup’s approximation into a state-space realization form. The original problem is then reformulated to fit the definition used in general-purpose optimal control problem (OCP) solvers such as RIOTS_95, a solver created as a Matlab toolbox. Illustrative examples from the literature are reproduced to demonstrate the effectiveness of the proposed methodology and a free final time OCP is also solved.

MSC:
49M25 Discrete approximations in optimal control
26A33 Fractional derivatives and integrals
Software:
Matlab; RIOTS_95
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