A numerical approximation for delay fractional optimal control problems based on the method of moments

In this paper, we present a method based upon the moments problem for solving a class of fractional optimal control problems (FOCPs) with time delay. The performance index of the FOCP is considered as a function of both the state and control variables and the dynamics of system is given as an ordinary fractional differential equation with time delay. The fractional derivative (FD) is described in the Riemann–Liouville sense in which the FD order is α ∈ (0, 1]. The main reason of using this technique is the convexification of a non-linear and non-convex FOCP with time delay in which the non-linearities in the control variable can be expressed as polynomials. The Grünwald–Letnikov formula is used as an approximation for FD in numerical computations. Some numerical examples are given to illustrate the effectiveness of our method.

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