Invariant Set

Invariant sets, subsets of a system's state space that remain unchanged under its dynamics, are central to analyzing system stability and safety. Current research focuses on developing methods to compute or approximate these sets, particularly for complex nonlinear systems, often employing reinforcement learning, model predictive control, or neural network-based approaches. This work is crucial for ensuring the safety and reliability of autonomous systems, such as robots and autonomous vehicles, and for improving the accuracy and efficiency of machine learning models applied to chaotic or high-dimensional data. The ability to identify and utilize invariant sets offers significant advancements in control theory, dynamical systems analysis, and machine learning.