Extend Learning-Based KKL Observers to Non-Autonomous Systems with Inputs

Develop learning-based Kazantzis–Kravaris/Luenberger (KKL) observer synthesis methods that handle exogenous input signals in non-autonomous nonlinear systems, thereby extending existing autonomous-only approaches to accommodate inputs explicitly.

Background

KKL observers require constructing an injective transformation that lifts nonlinear system dynamics into a stable quasi-linear latent space. While theory for non-autonomous systems shows the transformation must be time-varying to accommodate inputs, practical learning-based methods have largely focused on autonomous settings.

Prior learning-based KKL observer synthesis approaches rely on static transformation maps and do not explicitly model input-dependent dynamics, limiting their applicability when exogenous inputs alter system behavior. The paper identifies that extending these learning-based methods to handle inputs has remained an open problem and proposes HyperKKL as a step toward addressing it.