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

Year: 2025

Type: article

Abstract: This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on Genetic Programming, a variant of Genetic Algorithms where the search space is consists 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 optimization 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 identifies and optimizes Lyapunov functions for a wide range of systems, indicating a promising direction for automated stability proofs in engineering applications.

Source: Axioms

DOI: 10.3390/axioms14050343

Authors: Roman Pykhnivskyi, Anton Ryzhov, Andrii Sobchuk, Yurii Kravchenko

Institutions: Taras Shevchenko National University of Kyiv, State University of Information and Communication Technologies

Language: English

Topic: Evolutionary Algorithms and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W4409965500

FWCI:

Cites: 20

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Related to: 10