Control and verification of the safety-factor profile in Tokamaks using sum-of-squares polynomials

In this paper, we propose a method of using the sum-of-squares methodology to synthesize controllers for plasma stabilization in Tokamak reactors. We use a partial differential model of the poloidal magnetic flux gradient and attempt to stabilize a reference safety-factor profile. Our methods utilize full-state feedback control and are based on solving a dual version of the Lyapunov operator inequality. In addition, we implement the controller in-silico using experimental conditions inferred from the Tore Supra tokamak.