Nonlinear Stability

Nonlinear stability analysis focuses on understanding and guaranteeing the stability of systems whose behavior isn't linearly related to their inputs. Current research emphasizes developing robust methods for identifying and predicting the long-term behavior of complex nonlinear systems, employing techniques like look-ahead inference and mean-field control within models ranging from ordinary differential equations to neural networks. These advancements are crucial for improving the reliability and predictability of diverse applications, including ecological modeling, neuroscience, and the design of stable machine learning algorithms. The development of rigorous stability guarantees, particularly for learning-based control systems, is a key area of ongoing investigation.