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. Recent physics-informed learning approaches fuse prior knowledge, e.g., physics equations or smoothness assumptions, with flexible learning-based models, e.g., deep neural networks, but many open questions remain, for instance, in input-output data settings or in consistent model uncertainty quantification. This thesis contributes to this field by developing system identification tools for fusing input-output data with limited and diverse prior knowledge. Specifically, we will develop model structures and inference schemes to find accurate, uncertainty-quantifying system models while guiding learning 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. To ensure practical applicability, real-world experiments are conducted using typical academic benchmarks and full-scale industrial robots.
