MCM-2010: Estimation of Domains of Attraction: A Global Optimization Approach

G. MATALLANA PEREZ; A. BLANCO; A. BANDONI

MATHEMATICAL AND COMPUTER MODELLING

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2010 vol. 52 p. 574 - 585

0895-7177

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 potentialdummysolutions 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.