A robust MPC approach to the design of behavioural treatments

The objective of this paper is to provide some initial results on the application of control tools to the problem treatment design. Human behavior and reaction to treatment is complex and dependent on many unmeasurable external stimuli. Therefore, to the best of our knowledge, it cannot be described by simple models. Hence, one of the main messages in this paper is that, to design a treatment (controller) one cannot rely on exact models. More precisely, to be able to design effective treatments, we propose to use "simple" uncertain affine models whose response "covers" the most probable subject responses. So, we propose a simple model that contains two different types of uncertainties: one aimed at uncertainty of the dynamics and another aimed at approximating external perturbations that patients face in their daily life. With this model at hand, we design a robust model predictive controller, where one relies on the special structure of the uncertainty to develop efficient optimization algorithms.