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Suboptimal control of fractional-order dynamic systems with delay argument

In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement.