Kernel-Based Learning of Stable Nonlinear State-Space Models

This paper presents a kernel-based learning approach for black-box nonlinear state-space models with a focus on enforcing model stability. Specifically, we aim to enforce a stability notion called convergence which guarantees that, for any bounded input from a user-defined class, the model responses converge to a unique steady-state solution that remains within a positively invariant set that is user-defined and bounded. Such a form of model stability provides robustness of the learned models to new inputs unseen during the training phase. The problem is cast as a convex optimization problem with convex constraints that enforce the targeted convergence property. The benefits of the approach are illustrated by a simulation example.