3DoF-KF HMPC: A Kalman filter-based Hybrid Model Predictive Control Algorithm for Mixed Logical Dynamical Systems

This paper presents the formulation, design procedure, and application of a hybrid model predictive control (HMPC) scheme for hybrid systems that is embedded in a mixed logical dynamical (MLD) framework. The proposed scheme adopts a three degrees-of-freedom (3DoF) tuning method to accomplish precise setpoint tracking and ensure robustness in the face of disturbances (both measured and unmeasured) and uncertainty. Furthermore, the HMPC algorithm employs setpoint and disturbance anticipation to proactively enhance controller performance and potentially reduce control effort. Slack variables in the objective function prevent the mixed-integer quadratic problem from becoming infeasible. The effectiveness of the proposed algorithm is demonstrated through its application in three distinct case studies, which include control of production–inventory systems, time-varying behavioral interventions for physical activity, and management of epidemics/pandemic prevention. These case studies indicate that the HMPC algorithm can effectively manage hybrid dynamics, setpoint tracking and disturbance rejection in diverse and demanding circumstances, while tuned to perform well in the presence of nonlinearity and uncertainty. [Display omitted] Block diagram for 3DoF-KF HMPC, a Kalman filter-based HMPC scheme for setpoint tracking of a process subject to mixed logical dynamical constraints, measured and unmeasured disturbances. The controller receives filtered signals of measured disturbances and reference changes as inputs, and is formulated for independent, three degree-of-freedom tuning. •Hybrid systems modeled with an MLD framework are controlled using a robust MPC algorithm.•Two Kalman filters achieve independent 3DoF tuning of setpoints and disturbances.•The controller is configurable for different operation phases and anticipation.•Terminal cost, terminal constraints, and slack variables are part of the formulation.•Benefits are demonstrated in production-inventory systems, behavioral interventions, and epidemic control.