AUTONOMOUS CONTROL FOR STOCHASTIC SYSTEMS

Uncertainty is everywhere in the real world. A sudden power outage may occur at home; flights, packages, and emails may be delayed; and every commute involves pedestrians, cyclists, and vehicles whose behaviors are uncertain. Even our own choices can be uncertain, from what gift to buy for a friend, to what clothes to wear for the day. Despite this, people navigate daily life reasonably well because we can adapt, plan, and make reliable decisions even when our predictions are imperfect. It follows naturally that control and decision-making methods for cyberphysical/robotic autonomous systems should follow a similar principle. Probabilistic concepts like stochastic processes/differential equations provide core mathematical tools for modeling systems affected by random phenomena. In control systems engineering and its related subfields, such structured model-based methods are often interpretable and theoretically grounded, making it feasible to derive concrete guarantees for properties such as stability, safety, and robustness. However, many uncertain systems in practice are too complex to model exactly ("All models are wrong, but some are useful" -- Box, 1976). This has motivated data-driven, often model-free approaches based on artificial intelligence (AI), especially because of their strong representation and generalization abilities. At the same time, AI-based methods require high-quality data and substantial computation, and their lack of interpretability can make it difficult to certify stability, safety, or reliability under distribution shifts or faults. To achieve trustworthy autonomous control and decision-making under uncertainty, it is important to study the spectrum between model-based (structured) and model-free (data-driven) methods. The goal is to combine