Control Engineering Methods for the Design of Robust Behavioral Treatments

In this paper, a robust control approach is used to address the problem of adaptive behavioral treatment design. Human behavior (e.g., smoking and exercise) and reactions to treatment are complex and depend on many unmeasurable external stimuli, some of which are unknown. Thus, it is crucial to model human behavior over many subject responses. We propose a simple (low order) uncertain affine model subject to uncertainties whose response covers the most probable behavioral responses. The proposed model contains two different types of uncertainties: Uncertainty of the dynamics and external perturbations that patients face in their daily life. Once the uncertain model is defined, we demonstrate how least absolute shrinkage and selection operator (lasso) can be used as an identification tool. The lasso algorithm provides a way to directly estimate a model subject to sparse perturbations. With this estimated model, a robust control algorithm is developed, where one relies on the special structure of the uncertainty to develop efficient optimization algorithms. This paper concludes by using the proposed algorithm in a numerical experiment that simulates treatment for the urge to smoke.