Distributionally Robust Adaptive Control: Enabling Safe and Robust Reinforcement Learning

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Data-driven algorithms can autonomously control complex systems like autonomous cars and drones. However, the use of such powerful algorithms remains relegated primarily to controlled laboratory environments. The main reason for the minimal adoption of data-driven methods for safety-critical systems is the difficulty one encounters when attempting to establish safety and predictability guarantees as one would do with well-established control theoretical methods. This award supports fundamental research to identify the best methodologies to consolidate data-driven and control-theoretic tools so that the overall methodology is safe, robust, and high-performing. The new approach lifts control tools to speak the same language as the data-driven methods. In doing so, the performance of the data-driven methods is not compromised, and yet, the safety guarantees of control-theoretic tools can be constructed. Safe and predictable autonomous operation of complex systems can bring immense socio-economic benefits through its application in medical robotics, autonomous logistics, transportation, and extra-terrestrial exploration, to name a few. This research involves multiple disciplines, including robotics, control theory, statistical learning, and mathematics. The cross-disciplinary nature will assist underrepresented groups' broader participation in STEM and impact engineering education. To adopt data-driven methods that rely on reinforcement learning (RL) algorithms in safety-critical systems, we need guarantees on safety and robustness. Robust and adaptive control methodologies developed for classical systems with parametric uncertainties cannot be used directly in conjunction with RL because the latter operates on data-driven models for which identifying parametric and deterministic uncertainties is difficult, if not impossible. This research will construct a new class of robust adaptive controllers that are robust to errors in the learned distributions, thus allowing RL algorithms to directly interact with these controllers without further restrictions. Due to robustness at the level of distributions, notions of risk-aware safety can be included in a straightforward manner. This research will first aim to construct controllers that track temporally evolving state distributions with uniform bounds. Then, the epistemic uncertainties will be introduced with a novel adaptive control scheme to quantifiably control the effect of the uncertainties in the space of distributions. The results produced through this effort will bring the two distinct worlds of data-driven control and classical control together at a natural intersection point where trajectories of distributions, not of sample paths, are considered.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.