Set-based MPC with an application to enhanced local hyperthermia for cancer treatment

In this paper we propose a novel MPC scheme based on set theory that controls the temperature distribution in body tissue with the purpose of realizing local hyperthermia for improved cancer treatment. A new scheme is needed as there is no equilibrium nor invariant subset in the set of desirable temperature distributions subject to input and output constraints. The scheme fulfills the control objectives by using a dual-mode control strategy that steers the initial state to an appropriate reference set and keeps it inside the set of desirable temperature distributions for the (finite) length of the therapy duration. Feasibility of the scheme is guaranteed by off-line set-based computations. The online computations are formulated as standard quadratic programs. A numerical example is included to demonstrate the successful control of the transient temperature distribution in a one dimensional space.