Fractional optimal control problem of an axis-symmetric diffusion-wave propagation

Abstract

This paper presents the formulation of an axis-symmetric fractional optimal control problem (FOCP). Dynamic characteristics of the system are defined in terms of the left and right Riemann–Liouville fractional derivatives (RLFDs). The performance index of a FOCP is described with a state and a control function. Furthermore, dynamic constraints of the system are given by a fractional diffusion-wave equation. It is preferred to use the method of separation of variables for finding the analytical solution of the problem. In this way, the closed form solution of the problem is obtained by a linear combination of eigenfunctions and eigencoordinates. For numerical evaluation, the Grünwald–Letnikov approximation is applied to the problem. Consequently, some simulation results show that analytical and numerical solutions overlap for α=1. This numerical approach is applicable and effective for such a kind of FOCP. In addition, the changing of some variables related to the problem formulation is analyzed.