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We consider an improved model predictive control (MPC) formulation for linear hybrid systems described by mixed logical dynamical (MLD) models. The algorithm relies on a multiple-degree-of-freedom parametrization 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 objective function weights (such as move suppression) traditionally used in MPC schemes. The controller formulation is motivated by the needs of non-traditional control applications that are suitably described by hybrid production-inventory systems. Two applications are considered in this paper: adaptive, time-varying interventions in behavioral health, and inventory management in supply chains under conditions of limited capacity. In the adaptive intervention application, a hypothetical intervention inspired by the Fast Track program, a real-life preventive intervention for reducing conduct disorder in at-risk children, is examined. In the inventory management application, the ability of the algorithm to judiciously alter production capacity under conditions of varying demand is presented. These case studies demonstrate that MPC for hybrid systems can be tuned for desired performance under demanding conditions involving noise and uncertainty.

Control engineering offers a systematic and efficient means for optimizing the effectiveness of behavioral interventions. In this paper, we present an approach to develop dynamical models and subsequently, hybrid model predictive control schemes for assigning optimal dosages of naltrexone as treatment for a chronic pain condition known as fibromyalgia. We apply system identification techniques to develop models from daily diary reports completed by participants of a naltrexone intervention trial. The dynamic model serves as the basis for applying model predictive control as a decision algorithm for automated dosage selection of naltrexone in the face of the external disturbances. The categorical/discrete nature of the dosage assignment creates a need for hybrid model predictive control (HMPC) schemes. Simulation results that include conditions of significant plant-model mismatch demonstrate the performance and applicability of hybrid predictive control for optimized adaptive interventions for fibromyalgia treatment involving naltrexone. Index Termssystem identification; hybrid model predictive control; fibromyalgia; optimized behavioral interventions