Abstract: Data-driven and learning-based approaches have become an indispensable part of automation and autonomous systems. Control and planning components that are neural network models challenge existing principled methods for ensuring the reliability and safety of these systems. By taking a numerical and statistical perspective on synthesis and verification, it is possible to still prove strong properties for highly nonlinear systems with neural control policies.
To do so, we need to find value certificates, such as Lyapunov and barrier functions, that are themselves neural networks to capture the highly nonlinear value landscape of these systems. I will describe some of our work in this direction in different settings of nonlinear control design, including model-based stabilization, model-free reinforcement learning, and imitation learning from limited observations.