Set-Based Value Function Characterization and Neural Approximation of Stabilization Domains for Input-Constrained Discrete-Time Systems

This paper addresses the challenging problem of estimating domains of stabilization (DOSs) for nonlinear systems with input constraints. The authors propose a novel framework that combines set-based value function characterization with neural network approximation to compute stabilizing controllers and their associated stability regions. This approach targets general nonlinear discrete-time systems, providing a data-driven method to overcome traditional theoretical and computational limitations in stability analysis.