  In this thesis, we draw inspiration from both classical system identification
and modern machine learning in order to solve estimation problems for
real-world, physical systems. The main approach to estimation and learning
adopted is optimization based. Concepts such as regularization will be utilized
for encoding of prior knowledge and basis-function expansions will be used to
add nonlinear modeling power while keeping data requirements practical. The
thesis covers a wide range of applications, many inspired by applications
within robotics, but also extending outside this already wide field. Usage of
the proposed methods and algorithms are in many cases illustrated in the
real-world applications that motivated the research. Topics covered include
dynamics modeling and estimation, model-based reinforcement learning, spectral
estimation, friction modeling and state estimation and calibration in robotic
machining. In the work on modeling and identification of dynamics, we develop
regularization strategies that allow us to incorporate prior domain knowledge
into flexible, overparameterized models. We make use of classical control
theory to gain insight into training and regularization while using flexible
tools from modern deep learning. A particular focus of the work is to allow use
of modern methods in scenarios where gathering data is associated with a high
cost. In the robotics-inspired parts of the thesis, we develop methods that are
practically motivated and ensure that they are implementable also outside the
research setting. We demonstrate this by performing experiments in realistic
settings and providing open-source implementations of all proposed methods and
algorithms.
