Evolutionary Search for Polynomial Lyapunov Functions: A Genetic Programming Method for Exponential Stability Certification

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@Article{pykhnivskyi:2025:Axioms,

• author = "Roman Pykhnivskyi and Anton Ryzhov and Andrii Sobchuk and Yurii Kravchenko",
• title = "Evolutionary Search for Polynomial Lyapunov Functions: A Genetic Programming Method for Exponential Stability Certification",
• journal = "Axioms",
• year = "2025",
• volume = "14",
• number = "5",
• pages = "Article No. 343",
• keywords = "genetic algorithms, genetic programming",
• ISSN = "2075-1680",
• URL = "https://www.mdpi.com/2075-1680/14/5/343",
• DOI = "10.3390/axioms14050343",
• abstract = "This paper presents a method for constructing polynomial Lyapunov functions to analyse the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hierarchical tree structures. In our formulation, these polynomial functions are represented as binary trees. The Lyapunov conditions for exponential stability are interpreted as a minimax optimisation problem, using a carefully designed fitness metric to ensure positivity and dissipation within a chosen domain. The genetic algorithm then evolves candidate polynomial trees, minimizing constraint violations and continuously refining stability guarantees. Numerical examples illustrate that this methodology can effectively identify and optimise Lyapunov functions for a wide range of systems, indicating a promising direction for automated stability proofs in engineering applications.",
• notes = "also known as \cite{axioms14050343}",

}

Genetic Programming entries for Roman Pykhnivskyi Anton Ryzhov Andrii Sobchuk Yurii Kravchenko

Citations