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 variable. First, a reduced-order linear system is constructed at each equilibrium point using state, input, and output data. This step combines techniques from proper orthogonal decomposition, dynamic mode decomposition, and direct subspace 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 linear parameter-varying system approximates the nonlinear system even when the operating point changes in time.
|Original language||English (US)|
|Number of pages||16|
|Journal||International Journal of Robust and Nonlinear Control|
|State||Published - Mar 10 2017|
Bibliographical noteFunding Information:
This work was partially supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled ?CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms?. The work was also supported by the University of Minnesota Institute on the Environment, IREE Grant No. RS-0039-09. The first author gratefully acknowledges the financial support from the University of Minnesota through the 2015?16 Doctoral Dissertation Fellowship. The authors would also like to thank Joseph Nichols for discussions on this topic as well as help implementing the actuator disk example.
- dynamic mode decomposition
- reduced-order modeling