  Physics-informed machine learning (PIML) is a set of methods and tools that
systematically integrate machine learning (ML) algorithms with physical
constraints and abstract mathematical models developed in scientific and
engineering domains. As opposed to purely data-driven methods, PIML models can
be trained from additional information obtained by enforcing physical laws such
as energy and mass conservation. More broadly, PIML models can include abstract
properties and conditions such as stability, convexity, or invariance. The
basic premise of PIML is that the integration of ML and physics can yield more
effective, physically consistent, and data-efficient models. This paper aims to
provide a tutorial-like overview of the recent advances in PIML for dynamical
system modeling and control. Specifically, the paper covers an overview of the
theory, fundamental concepts and methods, tools, and applications on topics of:
1) physics-informed learning for system identification; 2) physics-informed
learning for control; 3) analysis and verification of PIML models; and 4)
physics-informed digital twins. The paper is concluded with a perspective on
open challenges and future research opportunities.
