A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem.