Many challenging plasma control problems still need to be addressed in order for the ITER plasma control system (PCS) to be able to maintain the plasma within a predefined operational space and optimize the plasma state evolution in the tokamak, which will greatly aid in the successful achievement of ITER's goals. Firstly in this work, a general control-oriented, physics-based modeling approach is developed to obtain first-principles-driven (FPD) models of the plasma magnetic profile and stored energy evolutions valid for high performance, high confinement (H-mode) scenarios, with the goal of developing model-based closed-loop algorithms to control the safety factor profile (q profile) and stored energy evolutions in the tokamak. The FPD model is tailored to H-mode burning plasma scenarios in ITER by employing the DINA-CH & CRONOS free-boundary tokamak simulation code, and the FPD model's prediction capabilities are demonstrated by comparing the prediction to data obtained from DINA-CH & CRONOS. Secondly, a model-based feedback control algorithm is designed to simultaneously track target q profile and stored energy evolutions in H-mode burning plasma scenarios in ITER by embedding the developed FPD model of the magnetic profile evolution into the control design process. The feedback controller is designed to ensure that the closed-loop system is robust to uncertainties in the electron density, electron temperature and plasma resistivity, and is tested in simulations with the developed FPD model. The effectiveness of the controller is demonstrated by first tracking nominal q profile and stored energy target evolutions, and then modulating the generated fusion power while maintaining the q profile in a stationary condition. In the process, many key practical issues for plasma profile control in ITER are investigated, which will be useful for the development of the ITER PCS that has recently been initiated. Some of the more pertinent investigated issues are the time necessary to drive the q profile and stored energy to a target evolution, and whether plasma control can be achieved through the use of separate individual control algorithms or whether a more fully integrated approach is required.