Optimal switching of MPC cost function for changing active constraints

Abstract

Model predictive control (MPC) allows for dealing with multivariable interactions, known future changes and dynamic satisfaction of constraints. Standard MPC has a cost function that aims at keeping selected controlled variables at constant setpoints. This work considers systems where the steady-state optimal active constraints change during operation. This situation is not handled optimally by standard MPC which uses fixed controlled variables for the unconstrained degrees of freedom. We propose a simple framework that detects the constraint changes and updates the controlled variables accordingly. The unconstrained controlled variables are chosen to be the reduced cost gradients, which when controlled to zero minimizes the steady-state economic cost. In this paper, the nullspace method for self-optimizing control is used to estimate the cost gradient using a static combination of the measurements. This estimated gradient is also used for detecting the current set of active constraints, which in particular allows for giving up constraints that were previously active. The proposed framework, here referred to as “region-based MPC”, is shown to be optimal for linear constrained systems with a quadratic economic cost function, and it allows for good economic performance in nonlinear systems in a neighborhood of the considered design points.