NONLINEAR DYNAMIC SYSTEMS DESIGN BASED ON THE OPTIMIZATION OF THE DOMAIN OF ATTRACTION

MATALLANA PEREZ LUIS GERÓNIMO; BLANCO ANÍBAL M.; BANDONI J. ALBERTO

MATHEMATICAL AND COMPUTER MODELLING

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2010 p. 731 - 745

0895-7177

In this paper it is proposed an optimization based methodology for the design of the operating equilibrium of a nonlinear dynamic system based on a measure of the extension of its domain of attraction. The approach consists in maximizing the radius of a ball in the states space contained in the region of negative definiteness of the time derivative of a quadratic Lyapunov function, using a two level optimization strategy. A deterministic global optimization problem is solved at the inner level to ensure proper estimation of the domain of attraction for each feasible realization of the design variables which are optimized at the outer level. In order to cope with the non differentiable nature of the inner problem, a stochastic algorithm is applied to manipulate the design variables at the outer level. The methodology is applied to several examples to illustrate different aspects of the approach.