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...
| Autores: | , , |
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| 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 |
| 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. |
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