Gaussian Process State-Space Models for Identification and Control of Dynamical Systems

Abstract

Model predictive control has enjoyed a lot of success in the past half a century due to its ability to consider complex multi-variable system dynamics, while simultaneously explicitly accounting for constraints. However, with the emergence of evermore complex nonlinear dynamical systems, physics-based modelling becomes increasingly impossible. Hence, there has been a shift towards data-driven identification in recent years. Nevertheless, the majority of the proposed data-driven methods rely on deterministic models that neglect the aleatoric uncertainty inherent to most dynamical systems and the epistemic uncertainty emerging from the estimation process itself, which can have detrimental consequences for safety-critical applications. Therefore, we aim to combine Gaussian process state-space models, which are built upon Bayesian inference in order to take both kinds of uncertainties in a principled manner into account, with a stochastic nonlinear model predictive control (SNMPC) framework. For this purpose, we examine various approximate uncertainty propagation approaches belonging to the randomized and the analytical categories, which are employed in the multi-step ahead prediction to satisfy probabilistic chance constraints. Putting everything together, we proposed an adaptive variant, which is able to collect the necessary training data automatically, while autonomously solving highly nonlinear control tasks in a safe and robust manner without requiring expert knowledge. We tested the robustness and performance properties of various (S)NMPC schemes on the linear double integrator system influenced by additive process noise, while the applicability of the ultimate adaptive variation of the SNMPC framework was shown on the pole swing-up and balance task of the famous cart-pole system affected by significant process noise.