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October 5, 2025Open Access

Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees

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Authors

JLJun LiuMFMaxwell Fitzsimmons

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Overview

Computational framework certifies asymptotic stability and safety in control systems, indicating practical applications.

Key Points

  • The method guarantees a smooth Lyapunov function for certifying safety and asymptotic stability.
  • A control barrier and control Lyapunov function pair ensures the existence of a certifying function.
  • The approach uses softmax relaxation for maximum barrier while refining via a guided technique.
  • Certified safe stabilization regions are often less conservative than traditional methods in practical scenarios.

Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/68e25559d6d66a53c2475268https://doi.org/10.48550/arxiv.2510.02223
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