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

arXiv:2604.00305 · eess.SY, cs.NE, cs.SY, math.DS, math.OC · Submitted 2026-03-31 · Read on arXiv

eess.SY, cs.NE, cs.SY, math.DS, math.OC

Submitted: 2026-03-31

Updated: 2026-09-18

Terminology

• Verification — 11× in this paper · explained in 2 episodes
• Lyapunov function — 10× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Closed-Loop System — 3× in this paper · explained in 4 episodes
• Formal Verification — 2× in this paper · explained in 2 episodes
• Neural Network Approximation — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Hybrid System — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• SMT solver — 1× in this paper · explained in 2 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

Sources

• Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Controls
• Lyapunov-stable neural-network control
• Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control
• Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation

Related papers

• One Request, Multiple Experts: LLM Orchestrates Domain Specific Models via Adaptive Task Routing
• A Geometric Decision Procedure for STL Feasibility and Repair
• Submodular Multi-Agent Policy Learning for Online Distributed Task Allocation in Open Multi-Agent Systems
• Policy-Level Recursive Self-Improvement for Embodied AI with a Criticality World Model
• Minimal Experiments for Robust Stabilization: Information, Spectral Geometry, and Duration
• Decentralized Power-Optimal Coordination for Spacecraft Swarms Using Time-Varying Magnetorquer Actuation