Design of switching multilinear model predictive control using gap metric

Abstract

Multilinear model predictive control is a strategy to track various set-points in a nonlinear process with a wide operating region, because it can predict the dynamic behavior of a part of the operating region using a linear model or weighted summation of linear models. In addition, it is computationally efficient compared to nonlinear model predictive control. The gap metric is exploited to evaluate the weights of linear models at each sampling time. In this work, we propose the design of local controllers for different operating regions using the gap metric, and prove that each local controller has the offset-free tracking property in the corresponding part of the operating region. We also construct a graph to find the optimal path from an initial point to a set-point and propose a switching strategy using the local controllers and the optimal path. It is proved that the resulting global controller can steer the state to anywhere in the operating region. A continuous stirred tank reactor process is studied to demonstrate the effectiveness of the proposed algorithms. Simulation studies show that the controllers designed by the proposed algorithm achieve the offset-tracking property when the initial point and the set-point are randomly chosen in the operating region.