# Data-driven Stabilization of Discrete-time Control-affine Nonlinear Systems: A Koopman Operator Approach

arXiv: https://arxiv.org/abs/2203.14114 · HTML: https://mlsanity.com/paper/2203.14114/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2022.

## Built on by (most cited first, 2 of 2)

- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Input-Side Variance Suppression under Non-Normal Transient Amplification in Continuous-Control Reinforcement Learning](https://mlsanity.com/paper/2604.17744/) (2026)

## Abstract (arXiv)

In recent years data-driven analysis of dynamical systems has attracted a lot of attention and transfer operator techniques, namely, Perron-Frobenius and Koopman operators are being used almost ubiquitously. Since data is always obtained in discrete-time, in this paper, we propose a purely data-driven approach for the design of a stabilizing feedback control law for a general class of discrete-time control-affine non-linear systems. In particular, we use the Koopman operator to lift a control-affine system to a higher-dimensional space, where the control system's evolution is bilinear. We analyze the controllability of the lifted bilinear system and relate it to the controllability of the underlying non-linear system. We then leverage the concept of Control Lyapunov Function (CLF) to design a state feedback law that stabilizes the origin. Furthermore, we demonstrate the efficacy of the proposed method to stabilize the origin of the Van der Pol oscillator and the chaotic Henon map from the time-series data.