Solving fractional optimal control problems using control vector parameterization

In this article, the control vector parameterization method is used to find optimal control laws of fractional systems. The proposed approach is based on the use of the fractional variational iteration method. Thus, first the control variable is parameterized by unknown coefficients to be determined, then its expression is substituted in the system state-space model. The resulting fractional ordinary differential equations are solved by the variational iteration method that provides an accurate approximate solution of the state variables. This solution is a function of time and the unknown coefficients. By substituting this solution into the performance index, the original fractional optimal control problem reduces to a nonlinear optimization problem where the unknown coefficients, introduced in the parameterization procedure, are the optimization variables. To find the optimal values of these coefficients, the Alienor global optimization method with the Optimization-Preserving-Operator method are used. The proposed approach is illustrated by an application example.