Online Constrained Bayesian Inference and Learning of Gaussian-Process State-Space Models

Recent research has shown that it is possible to perform online learning of nonlinear dynamical systems. Furthermore, the results suggest that combining approximate Gaussian-process (GP) regression with model-based estimators, such as Kalman filters and particle filters (PFs), leads to efficient learners under the GP-state-space model (GP-SSM) framework. Here, we analyze how learning of GP-SSMs can be done when there are constraints on the system to be learned. Our analysis is based on a recently developed online PF-based learning method, where the GP-SSM is expressed as a basis-function expansion. We show that the method by adaptation of the basis functions can satisfy several constraints, such as symmetry, antisymmetry, Neumann boundary conditions, and linear operator constraints. A Monte-Carlo simulation study indicates reduced estimation errors with more than 50%.