Estimation of domains of attraction: A global optimization approach

In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time der...

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Detalhes bibliográficos
Autores: Matallana Perez, Luis Geronimo, Blanco, Anibal Manuel, Bandoni, Jose Alberto
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/55939
Acesso em linha:http://hdl.handle.net/11336/55939
Access Level:acceso abierto
Palavra-chave:DOMAINS OF ATTRACTION
GLOBAL OPTIMIZATION
LYAPUNOV FUNCTION
NONLINEAR DYNAMIC SYSTEMS
https://purl.org/becyt/ford/2.4
https://purl.org/becyt/ford/2
Descrição
Resumo:In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.