Joint state and dynamics estimation with high-gain observers and Gaussian process models

Abstract

With the rising complexity of dynamical systems generating ever more data, learning dynamics models appears as a promising alternative to physics-based modeling. However, the data available from physical platforms may be noisy and not cover all state variables. Hence, it is necessary to jointly perform state and dynamics estimation. In this paper, we propose interconnecting a high-gain observer and a dynamics learning framework, specifically a Gaussian process state-space model. The observer provides state estimates, which serve as the data for training the dynamics model. The updated model, in turn, is used to improve the observer. Joint convergence of the observer and the dynamics model is proved for high enough gain, up to the measurement and process perturbations. Simultaneous dynamics learning and state estimation are demonstrated on simulations of a mass-spring-mass system.

Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs

“…Observers often assume a good dynamics model, but designs that can deal with imperfect models are also available. In that case, the unknown parts of the dynamics can be overridden through high-gain or sliding-mode designs to enable convergence (Buisson-Fenet et al, 2021;Shtessel et al, 2016). Otherwise, the unknown parameters can be seen as extra states with constant dynamics, and extended state observers can be designed, such that the estimated state and parameters converge asymptotically (Praly et al, 2006).…”

Adaptive Nonlinear Regulation via Gaussian Process

“…Moreover, since GPs allow for analytical formulations, theoretical guarantees on the a posteriori can be drawn directly from the collected data [24], [25]. Recently, GP models spread inside the field of nonlinear optimal control [26], with several applications to the particular case of Model Predictive Control (MPC) [27], [28], and inside the field of nonlinear observers [29].…”

Estimating States and Model Uncertainties Jointly by a Sparsity Promoting UKF

“…Wan et al (1999), but only few studies on filter approaches dealing with complex model uncertainties and their detection have been carried out so far. Recently, only Khajenejad et al (2021), Buisson-Fenet et al (2021) and Kullberg et al (2021) investigated situations when just a partial model of the system is known. Khajenejad et al (2021) utilize a complex geometrical approach to estimate an upper and lower barrier for the approximated state to lie in between.…”

“…In Buisson-Fenet et al (2021), a high gain observer is deployed to estimate states that are then utilized to infer a Gaussian process model of the plant. Subsequently, the model is used within the observer and vice versa, affecting and correlating with each other.…”

“…In this work, we start from a problem formulation similar to Khajenejad et al (2021), Buisson-Fenet et al (2021 and Kullberg et al (2021) and define a joint state, that additionally contains parameters of the linear combinations for the partial dynamics to be approximated. However, we use a square-root UKF (SQ-UKF) combined with a physics-motivated library for the linear combinations, simplifying the inference of physical coherences.…”