Data-driven model predictive control using interpolated koopman generators

Sebastian Peitz, Samuel E. Otto, Clarence W. Rowley

Research output: Contribution to journalArticlepeer-review

Abstract

In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation via dynamic mode decomposition, a quantization approach was recently proposed in [S. Peitz and S. Klus, Automatica J. IFAC, 106 (2019), pp. 184- 191]. This way, control of nonlinear dynamical systems can be realized by means of switched systems techniques, using only a finite set of autonomous Koopman operator-based reduced models. These individual systems can be approximated very efficiently from data. The main idea is to transform a control system into a set of autonomous systems for which the optimal switching sequence has to be computed. In this article, we extend these results to continuous control inputs using relaxation. This way, we combine the advantages of the data efficiency of approximating a finite set of autonomous systems with continuous controls, as the data requirements increase only linearly with the input dimension. We show that when using the Koopman generator, this relaxation-realized by linear interpolation between two operators-does not introduce any error for control affine systems. This allows us to control high-dimensional nonlinear systems using bilinear, low-dimensional surrogate models. The efficiency of the proposed approach is demonstrated using several examples with increasing complexity, from the Duffing oscillator to the chaotic fluidic pinball.

Original languageEnglish (US)
Pages (from-to)2162-2193
Number of pages32
JournalSIAM Journal on Applied Dynamical Systems
Volume19
Issue number3
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

  • Dynamic mode decomposition
  • Koopman operator
  • Model predictive control
  • Optimal control
  • Reduced order modeling

Fingerprint Dive into the research topics of 'Data-driven model predictive control using interpolated koopman generators'. Together they form a unique fingerprint.

Cite this