English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In recent years, the success of the Koopman operator in dynamical systemsanalysis has also fueled the development of Koopman operator-based controlframeworks. In order to preserve the relatively low data requirements for anapproximation via Dynamic Mode Decomposition, a quantization approach wasrecently proposed in [Peitz \& Klus, Automatica 106, 2019]. This way, controlof nonlinear dynamical systems can be realized by means of switched systemstechniques, using only a finite set of autonomous Koopman operator-basedreduced models. These individual systems can be approximated very efficientlyfrom data. The main idea is to transform a control system into a set ofautonomous systems for which the optimal switching sequence has to be computed.In this article, we extend these results to continuous control inputs usingrelaxation. This way, we combine the advantages of the data efficiency ofapproximating a finite set of autonomous systems with continuous controls. Weshow that when using the Koopman generator, this relaxation --- realized bylinear interpolation between two operators --- does not introduce any error forcontrol affine systems. This allows us to control high-dimensional nonlinearsystems using bilinear, low-dimensional surrogate models. The efficiency of theproposed approach is demonstrated using several examples with increasingcomplexity, from the Duffing oscillator to the chaotic fluidic pinball.

Data-Driven Model Predictive Control using Interpolated Koopman Generators