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

Abstract

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.

A dynamical systems model for improving gestational weight gain behavioral interventions

“…We are currently using the model to evaluate decision rules that will enable time-varying, adaptive behavioral interventions [7], [8] to manage GWG, particularly for the case of overweight and obese women; these will ultimately lead to hybrid model predictive control algorithms as decision policies [9]. Well-designed clinical trials will be required in order to accomplish the system identification tasks that will validate the model and enable the reallife implementation of decision rules and hybrid MPC for this problem.…”

“…3, with inflows corresponding to the exogenous variables ξ 1 , ξ 2 , and ξ 3 . To generate the dynamical system description, the principle of conservation of mass is applied to each inventory, from which a system of differential equations can be obtained: (5) (6) (7) (8) (9) τ i are time constants, θ i time delays, and ζ i disturbances. In this dynamical representation, the regression weights β ij and γ ij from the structural equation model correspond to gains of the system.…”

“…Decision rules operationalize these changes, which can correspond to eliminating or adding some intervention components based on participant response during the intervention, or altering the dosage of existing components (for example, increasing the number of physical activity sessions). Adaptive, time-varying interventions constitute feedback control systems [8] and are amenable to hybrid model predictive control approaches [9]. Developing optimal decision rules based on hybrid MPC constitutes a future activity in this work.…”

“…To meet this need, there has been an increasing interest in the design and implementation of adaptive behavioral interventions using dynamical systems and control engineering methods to increase intervention effectiveness and improve participant response [7], [8]. In this paper we consider the initial problem of modeling the dynamics of such an intervention, with the long-term goal of designing, and ultimately implementing, an optimized behavioral intervention based on modern control engineering concepts, such as hybrid model predictive control [9]. The overall simulation model for GWG developed in this paper can be divided into four main segments ( Fig.…”

Hybrid model predictive control for optimizing gestational weight gain behavioral interventions

“…In an adaptive intervention, dosages of intervention components are assigned to participants based on values of tailoring variables. The use of dynamical systems and control engineering methods to optimize adaptive behavioral interventions is described in [8], [9].…”