Fractional optimal control problem of a distributed system in cylindrical coordinates

In this work, Fractional Optimal Control Problem (FOCP) of a Distributed system is investigated in cylindrical coordinates. Axis-symmetry naturally arises in the problem formulation. The fractional time derivative is described in the Riemann–Liouville (RL) sense. The performance index of a FOCP is considered as a function of state and control variables and system dynamics are given as a Partial Fractional Differential Equation (PFDE). The method of separation of variables is used to find the solution of the problem. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computations, Grünwald–Letnikov (GL) approach is used. A time-invariant example is considered to demonstrate the effectiveness of the formulation. The comparison of analytical and numerical solutions is given using simulation results and also it can be seen that analytical and numerical results converge each other. In addition, simulation results for different values of order of derivative, time discretizations and eigenfunctions are analyzed.