Evolutionary Search for Polynomial Lyapunov Functions: A Genetic Programming Method for Exponential Stability Certification
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- @Article{pykhnivskyi:2025:Axioms,
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author = "Roman Pykhnivskyi and Anton Ryzhov and
Andrii Sobchuk and Yurii Kravchenko",
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title = "Evolutionary Search for Polynomial Lyapunov Functions:
A Genetic Programming Method for Exponential Stability
Certification",
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journal = "Axioms",
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year = "2025",
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volume = "14",
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number = "5",
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pages = "Article No. 343",
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keywords = "genetic algorithms, genetic programming",
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ISSN = "2075-1680",
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URL = "
https://www.mdpi.com/2075-1680/14/5/343",
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DOI = "
10.3390/axioms14050343",
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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