info:eu-repo/semantics/article
Estimation of domains of attraction: A global optimization approach
Fecha
2010-08Registro en:
Matallana Perez, Luis Geronimo; Blanco, Anibal Manuel; Bandoni, Jose Alberto; Estimation of domains of attraction: A global optimization approach; Pergamon-Elsevier Science Ltd; Mathematical And Computer Modelling; 52; 3-4; 8-2010; 574-585
0895-7177
CONICET Digital
CONICET
Autor
Matallana Perez, Luis Geronimo
Blanco, Anibal Manuel
Bandoni, Jose Alberto
Resumen
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.