Initial Application of SONC to Lyapunov Stability of Dynamical Systems

Autor:	Heuer, Janin, de Wolff, Timo
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Mathematics - Algebraic Geometry 12D15 14P99 90C26 90C30 93D05 93D30 37C75
Druh dokumentu:	Working Paper
Popis:	Certifying the stability of dynamical systems is a central and challenging task in control theory and systems analysis. To tackle these problems we present an algorithmic approach to finding polynomial Lyapunov functions. Our method relies on sums of nonnegative circuit functions (SONC), a certificate of nonnegativity of real polynomials. We show that both the problem of verifying as well as the more difficult task of finding Lyapunov functions can be carried out via relative entropy programming when using SONC certificates. This approach is analogue yet independent to finding Lyapunov functions via sums of squares (SOS) certificates and semidefinite programming. Furthermore, we explore whether using the related, recently introduced DSONC certificate is advantageous compared to SONC for this type of problem. We implemented our results, and present examples to show their applicability. Comment: 24 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.02031 Zobrazit plný text záznamu View this record from Arxiv