Application of gap metric to model bank determination in multilinear model approach

This paper presents a gap metric based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system when multilinear model approach is employed to design a controller for this nonlinear system. For a prescribed distance level, the minimum linear model bank determined by the proposed method can provide sufficient information for multilinear model controller design of the nonlinear system. To illustrate the usefulness of the proposed method, two examples of nonlinear systems are presented. Moreover, a mixed logical dynamical model-based MPC (MLD–MPC) controller is designed based on the minimum model bank. Simulations confirm the method for selecting linear model bank in multilinear model approach.