While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics.

Nico (right) and Matteo Mucchetti pose with their homemade dark ride vehicle. We may earn revenue from the products available on this page and participate in affiliate programs. When 12-year-old Matteo Mucchetti mapped out an amusement-style attraction that he wanted to create in his family's basement and then showed it to his older brother Nico, the high-school sophomore was immediately sold. "This is amazing," said Nico. "Let's make it!" Matteo had sketched on paper a top-down view of the multi-room space in Bear, Delaware, where they live.

If the memory state can be addressed by its content, itisfurthermore called content-addressable.

However, finding Lyapunov functions for general nonlinear systems is a challenging task.

Behavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning.