Learning a Contracting KKL-observer with Local Optimal Guarantees
For nonlinear state estimation, this work provides a principled way to design KKL observers with both stability and optimality guarantees, though it is an incremental improvement over existing KKL observer methods.
This paper proposes a method to learn a KKL observer that guarantees global stability and local optimality by mimicking a Minimum Energy Estimator, validated through simulations on nonlinear benchmarks.
The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers relies heavily on the specific choice of these latent dynamics, which is often heuristic. This paper proposes a methodology to learn a KKL observer that combines global stability guarantees with local optimality. We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property. The proposed strategy is validated through numerical simulations on nonlinear benchmarks, demonstrating a good performance in the presence of state and measurement noise.