Integration of design and NMPC-based control for chemical processes under uncertainty: An MPCC-based framework

Abstract

The use of nonlinear model predictive control (NMPC) for the integration of design and control remains as an open area of research. When NMPC is incorporated into the framework for design and control, this results into a bilevel problem formulation. The search of a solution for a bilevel problem is often carried out with the implementation of systematic iterative methodologies. In this work, we implement the classical KKT transformation strategy to transform the original bilevel problem for simultaneous design and NMPC-based control into a single-level dynamic optimization problem. This single-level formulation is referred to as a mathematical program with complementarity constraints (MPCC). Violations to constraint qualifications (CQs) are avoided through the implementation of several reformulation techniques. This facilitates the convergence of the MPCC for optimal design and control. The use of an MPCC-based formulation allows to fully incorporate the NMPC’s necessary conditions for optimality into the design problem as a set of algebraic constraints. Accordingly, the MPCC is solved as a conventional NLP, i.e., we avoid the use of decomposition or simplification methodologies for the solution of the bilevel problem. This guarantees optimality in the solution for integrated design and NMPC-based control. This strategy was implemented in three case studies involving small, medium-scale, and highly nonlinear systems to demonstrate the application of MPCCs for design and NMPC-based control under process disturbances and uncertainty.