Theoretical and algorithmic advances in multi‐parametric programming and control

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi‐parametric programming and explicit/multi‐parametric model predictive control (mp‐MPC). In multi‐parametric programming, advances include areas such as nonlinear multi‐parametric programming (mp‐NLP), bi‐level programming, dynamic programming and global optimization for multi‐parametric mixed‐integer linear programming problems (mp‐MILPs). In multi‐parametric/explicit MPC (mp‐MPC), advances include areas such as robust multi‐parametric control, multi‐parametric nonlinear MPC (mp‐NMPC) and model reduction in mp‐MPC. A comprehensive framework for multi‐parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.