Control of safety factor profile in infinite dimension tokamak plasmas

The increasing energy needs of the world population require the development, the control and the supply of new forms of energy. In this context, nuclear fusion is a track of extremely promising research. World project ITER is intended to prove the scientific and technical feasibility of nuclear fusion. One of the many key-goal is the control of the current profile spatial distribution in plasmas of tokamak, which is one of the main parameter for the stability and the performance of the experiments. The spatio-temporal evolution of this current is described by a set of nonlinear partial differential equations. In this document stabilization is proposed considering robust control of current profile spatial distribution in infinite dimension. Two approaches are proposed: the first one is based on sliding mode approach and the second one (of type proportional and proportional integral) is based on the Lyapunov functions in infinite dimension. The design of the control law is based on the 1D equation resistive diffusion of the magnetic flux. The control laws are calculated in infinite dimension without space discretization. (author)