The methodology and the up-to-date results concerning the solution to the problem of plasma position and shape control in the International Thermonuclear Experimental Reactor (ITER) are presented. Attention is focused on the burn phase of the operation scenario, when the control objectives are particularly stringent. The aim is to control up to six distances (gaps) between the plasma separatrix and the plasma-facing components. The control algorithm is designed within a linear quadratic Gaussian optimal control framework. Linear and nonlinear simulations show the performance of the controller in the presence of plasma vertical position offsets, beta drops, and power supply voltage saturation.