A novel model predictive control formulation for hybrid systems with application to adaptive behavioral interventions

This paper presents a novel model predictive control (MPC) formulation for linear hybrid systems. The algorithm relies on a multiple-degree-of-freedom formulation that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed-loop system. Consequently, controller tuning is more flexible and intuitive than relying on move suppression weights as traditionally used in MPC schemes. The formulation is motivated by the need to achieve robust performance in using the algorithm in emerging applications, for instance, as a decision policy for adaptive, time-varying interventions used in behavioral health. The proposed algorithm is demonstrated on a hypothetical adaptive intervention problem inspired by the Fast Track program, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results in the presence of simultaneous disturbances and significant plant-model mismatch are presented. These demonstrate that a hybrid MPC-based approach for this class of interventions can be tuned for desired performance under demanding conditions that resemble participant variability that is experienced in practice when applying an adaptive intervention to a population.