  In this paper, we consider an open-loop, finite-time, optimal control problem
of attaining a specific desired current profile during the ramp-up phase by
finding the best open-loop actuator input trajectories. Average density, total
power, and plasma current are used as control actuators to manipulate the
profile shape in tokamak plasmas. Based on the control parameterization method,
we propose a numerical solution procedure directly to solve the original
PDE-constrained optimization problem using gradient-based optimization
techniques such as sequential quadratic programming (SQP). This paper is aimed
at proposing an effective framework for the solution of PDE-constrained
optimization problem in tokamak plasmas. A more user-friendly and efficient
graphical user interface (GUI) is designed in MATLAB and the numerical
simulation results are verified to demonstrate its applicability. In addition,
the proposed framework of combining existing PDE and numerical optimization
solvers to solve PDE-constrained optimization problem has the prospective to
target challenge advanced control problems arising in more general chemical
engineering processes.
