Computational optimal control for the time fractional convection-diffusion-reaction system

Abstract

This paper proposes a numerical approximation method for computational optimal control of a time fractional convection-diffusion-reaction system. The proposed method involves discretizing the spatial domain by finite element method, approximating the admissible controls by control parameterization, and then obtaining an optimal parameter selection problem which can be solved by numerical optimization algorithms such as sequential quadratic programming. Specifically, an implicit finite difference method is employed to solve the time fractional system, and the sensitivity method for gradient computation in integer order optimal control problems is adjusted to the fractional order case. Simulation results demonstrate the validity and accuracy of the proposed numerical approximation method.