Safe Learning-based Observers for Unknown Nonlinear Systems using Bayesian Optimization
This work addresses the challenge of safe and efficient state estimation in control systems, offering a novel approach with incremental improvements over existing methods.
The paper tackles the problem of designing state observers for unknown nonlinear systems by proposing a modular method that ensures safety during learning and improves convergence rates, demonstrating its potential on a benchmark system with performance guarantees.
Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper, a modular design methodology is formulated, that consists of three design phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Bayesian optimization and Gaussian processes; and, (iii) a re-design phase that leverages the learned dynamics to improve convergence rate of the state estimation error. The potential of our proposed learning-based observer is demonstrated on a benchmark nonlinear system. Additionally, certificates of guaranteed estimation performance are provided.