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This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]