  We present an historical overview about the connections between the analysis
of risk and the control of autonomous systems. We offer two main contributions.
Our first contribution is to propose three overlapping paradigms to classify
the vast body of literature: the worst-case, risk-neutral, and risk-averse
paradigms. We consider an appropriate assessment for the risk of an autonomous
system to depend on the application at hand. In contrast, it is typical to
assess risk using an expectation, variance, or probability alone. Our second
contribution is to unify the concepts of risk and autonomous systems. We
achieve this by connecting approaches for quantifying and optimizing the risk
that arises from a system's behaviour across academic fields. The survey is
highly multidisciplinary. We include research from the communities of
reinforcement learning, stochastic and robust control theory, operations
research, and formal verification. We describe both model-based and model-free
methods, with emphasis on the former. Lastly, we highlight fruitful areas for
further research. A key direction is to blend risk-averse model-based and
model-free methods to enhance the real-time adaptive capabilities of systems to
improve human and environmental welfare.
