Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control

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 behavior 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.