Safe learning-based observers for unknown nonlinear systems using Bayesian optimization

Abstract

In this paper, a modular observer design methodology is formulated for nonlinear systems with partial model knowledge. Our design consists of three 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 Gaussian process-based Bayesian optimization; 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.