An Improved Formulation of Hybrid Model Predictive Control With Application to Production-Inventory Systems

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 nontraditional 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.