Linear observer synthesis for nonlinear systems using Koopman Operator framework

By Amit Surana, Andrzej Banaszuk. 2016

193 citations recorded by the source corpus.

Abstract: In this paper we develop a new approach for observer synthesis for discrete time autonomous nonlinear systems based on Koopman operator theoretic framework. Koopman operator is a linear but an infinite-dimensional operator that governs the time evolution of system outputs in a linear fashion. We exploit this property to synthesize an observer form which enables the use of Luenberger/Kalman-like linear observers for nonlinear estimation. Using the techniques for Koopman eigenvalue/eigenfunction/mode computation, we describe a numerical procedure to construct such an observer form which is often valid in a large portion of state space or even globally. We numerically compare our approach with Extended Kalman Filter and report superior performance.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/800c5dd84b335091b2f4099bc560588f41e22051

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

1. Steven L. Brunton
2. J. Nathan Kutz
3. Bingni W. Brunton
4. Krithika Manohar
5. Igor Mezi'c
6. Milan Korda
7. Maizar Raissi
8. G. Em Karniadakis

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Igor Mezi'c
4. Bingni W. Brunton
5. Milan Korda
6. Krithika Manohar
7. Joshua L. Proctor
8. Maizar Raissi

In Statistics and Probability

1. J. Nathan Kutz
2. Steven L. Brunton
3. Milan Korda
4. Bingni W. Brunton
5. Igor Mezi'c
6. Krithika Manohar
7. Joshua L. Proctor
8. Maizar Raissi

Citations in the corpus

• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control (2016, methodology): “This idea is closely related to the use of the Koopman operator for state estimation [22, 21].”
• On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator (2017, methodology): “This concept was succesfully applied to model predictive control in [13] and to state estimation in [24].”
• Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “mators [79], [80] and controllers [81], although establishing rigorous connections to control theory is an ongoing effort [82], [83], [84].”