Data-Driven Plant-Model Mismatch Quantification in Input-Constrained Linear MPC

In this paper, we present a novel data-driven approach for estimating plant-model mismatch for linear MIMO systems operating under constrained MPC. We begin with analyzing the closed-loop plant data; under the assumption that changes in the active set of constraints of the controller are due to (low frequency) setpoint changes, we separate the data into a finite number of fixed active set (FAS) subsets, each of which features a time-invariant active set of MPC constraints. We establish an explicit relationship relating the magnitude of plant-model mismatch to the autocovariance of the system output in the FAS case, while accounting for changes in the setpoint value. The mismatch estimation problem is then formulated as a global optimization calculation, aimed at minimizing the discrepancy between the autocovariance estimated using this theoretical tool, and the autocovariance of plant outputs computed from operating data for each FAS subset. A chemical process case study is presented to illustrate the effectiveness of the approach.