Learning Stable Koopman Embeddings
This addresses the challenge of ensuring stability in data-driven nonlinear system modeling, which is important for control and robotics applications, though it appears incremental as it builds on existing Koopman embedding approaches.
The paper tackles the problem of learning stable models of nonlinear systems by proposing a data-driven method that uses Koopman embeddings to lift the state space to a linear manifold, proving that all discrete-time nonlinear contracting models can be learned in this framework. The result is a method that allows unconstrained optimization while enforcing stability, simplifying computations.
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that every discrete-time nonlinear contracting model can be learnt in our framework. Another significant merit of the proposed approach is that it allows for unconstrained optimization over the Koopman embedding and operator jointly while enforcing stability of the model, via a direct parameterization of stable linear systems, greatly simplifying the computations involved. We validate our method on a simulated system and analyze the advantages of our parameterization compared to alternatives.