Kernel-Based Identification of Incrementally Input-to-State Stable Nonlinear Systems

Methods based on Reproducing Kernel Hilbert Spaces (RKHS) have proven to be a valuable tool for the identification of linear time-invariant systems in both discrete- and continuous-time. In particular, unlike most other techniques, they enable to systematically confer a priori desirable properties, such as stability, on the estimated models. However, existing RKHS methods mainly target impulse responses and, hence, do not extend well to the context of nonlinear systems. In this work, we propose a novel RKHS-based methodology for the identification of discrete-time nonlinear systems guaranteeing that the identified system is incrementally input-to-state stable (δISS). We model the identified system using a predictor function that, given past input and output samples, yields the output prediction at the next time instant. The predictor is selected from an RKHS by solving a constrained optimization problem that guarantees its δISS properties. The proposed approach is validated via numerical simulations.