Exploiting Prior Knowledge for Structured Learning and Inference in Dynamical Systems

Accurate and well-generalizing system models are a cornerstone for analysis and reliable control of complex dynamical systems in changing environments, e.g., intelligent autonomous robots, vehicles in unknown environments, or even disease outbreaks. While solely physics-based models lack the flexibility to represent the full complexity of the system dynamics, data- and learning-based models are usually data-inefficient and suffer from poor generalization. Recently, physics-informed learning for fusing both, prior knowledge, e.g., physics equations, or smoothness assumptions, and flexible learning-based models, e.g., deep neural networks, has shown promising results in resolving these issues. However, the resulting methods typically rely on full state measurements, and require certain types of prior knowledge, preventing the fusion of all prior information that may be available. Moreover, a consistent quantification of model uncertainty, e.g., for use in robust or stochastic control, is often not provided. These limitations prevent, among others, the construction of accurate and yet well-generalizing system models that would enable complex dynamical systems, for instance in robotics, to operate accurately and truly autonomously under challenging and changing conditions. This thesis contributes to this vision by providing system identification tools for fusion of input-output data with limited and diverse prior knowledge. Specifically, we will develop model structures and inference schemes for finding accurate, uncertainty-quantifying system models while guiding the learning process with different types of prior knowledge to achieve reliable generalization, data efficiency, and adaptivity. Towards this end, we will formulate constrained learning-based models to incorporate different types of prior knowledge, such as explicit physics equations, smoothness assumptions, or system topology knowledge. In conjunction, we develop Bayesian schemes to enable joint inference of latent states and learning of unknown parameters based on input-output data. To account for changing system and environment conditions, automatic strategies for finding adaptive models from data are developed. We analyze the accuracy, generalization capability, and adaptivity of models as well as the data efficiency and convergence of inference schemes both theoretically and empirically. To ensure practical relevance, real-world experiments with typical academic benchmarks as well as with full-scale industrial robots are conducted.