A method to construct reduced-order parameter varying models

This paper describes a method to construct reduced-order models for high dimensional nonlinear systems. It is assumed that the nonlinear system has a collection of equilibrium operating points parameterized by a scheduling parameter. First, a reduced-order linear system is constructed at each equilibrium point using input/output data. This step combines techniques from dynamic mode decomposition and direct subspace system identification. This yields discrete-time models that are linear from input to output but whose state matrices are functions of the scheduling parameter. Second, a parameter varying linearization is used to connect these linear models across the various operating points. The key technical issue in this second step is to ensure the reduced-order model has a consistent state definition across all operating points. These two steps yield a reduced-order Linear Parameter Varying (LPV) system that approximates the nonlinear system even when the operating point changes in time. Copyright c © 2015 John Wiley & Sons, Ltd.