A Stable and Robust NMPC Strategy with Reduced Models and Nonuniform Grids

Nonuniform discretizations of state and control profiles and model reduction are essential to approximate discretized DAE systems, capture multiple time scales of the state profiles and reduce the size of nonlinear programming (NLP) subproblems for off-line optimal control problems. These discretizations are often dictated by dynamic characteristics that depend on the system application. However, nonuniform grids in Nonlinear MPC (NMPC), which we denote as input and state blocking strategies, may not lead to recursive feasibility, a key property for nominal stability that follows directly with uniform grids. In this study, we analyze a class of NMPC blocking strategies and show that nominal stability and input-to-state stability (ISS) can be preserved with these formulations. These strategies are especially useful for large first principles models, as we demonstrate on a bubbling fluidized bed (BFB) process that captures CO2 from flue gas. With this case study we demonstrate that input and state blocking, along with model reduction, leads to accurate state profiles, nominal and robust stability, far less computation, and essentially the same NMPC performance as with uniform grids.