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cover Domain of Attraction [Analy...
Domain of Attraction [Analysis and Control via SOS Programming
Springer London 2011

The stability of equilibrium points plays a fundamental role in dynamical systems. For nonlinear dynamical systems, which represent the majority of real plants, an investigation of stability requires the characterization of the domain of attraction (DA) of an equilibrium point, i.e., the set of initial conditions from which the trajectory of the system converges to such a point. It is well-known that estimating the DA, or even more attempting to control it, are very difficult problems because of the complex relationship of this set with the model of the system. The book also offers a concise and simple description of the main features of SOS programming which can be used in research and teaching. In particular, it introduces various classes of SOS polynomials and their characterization via LMIs and addresses typical problems such as establishment of positivity or non-positivity of polynomials and matrix polynomials, determining the minimum of rational functions, and solving systems of polynomial equations, in cases of both unconstrained and constrained variables. The techniques presented in this book are available in the MATLAB® toolbox SMRSOFT, which can be downloaded from http://www.eee.hku.hk/~chesi. Domain of Attraction addresses the estimation and control of the DA of equilibrium points using the novel SOS programming scheme, i.e., optimization techniques that have been recently developed based on polynomials that are sums of squares of polynomials (SOS polynomials) and that amount to solving convex optimization problems with linear matrix inequality (LMI) constraints, also known as semidefinite programs (SDPs). For the first time in the literature, a means of dealing with these issues is presented in a unified framework for various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial systems, uncertain polynomial systems, and nonlinear (possibly uncertain) non-polynomial systems. The methods proposed in this book are illustrated in a variety of real systems and simulated systems with randomly chosen structures and/or coefficients which includes chemical reactors, electric circuits, mechanical devices, and social models. The book also offers a concise and simple description of the main features of SOS programming which can be used in research and teaching. In particular, it introduces various classes of SOS polynomials and their characterization via LMIs and addresses typical problems such as establishment of positivity or non-positivity of polynomials and matrix polynomials, determining the minimum of rational functions, and solving systems of polynomial equations, in cases of both unconstrained and constrained variables. The techniques presented in this book are available in the MATLAB® toolbox SMRSOFT, which can be downloaded from http://www.eee.hku.hk/~chesi

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Título:
Domain of Attraction [ Recurso electrónico-En línea] : Analysis and Control via SOS Programming / by Graziano Chesi
Editorial:
London : Springer London, 2011
Descripción física:
XVIII, 286p. 46 illus. : digital
Tipo Audiovisual:
Engineering
Systems theory
Physics
Engineering
Control
Systems Theory, Control
Nonlinear Dynamics
Complexity
Mención de serie:
Lecture Notes in Control and Information Sciences, 0170-8643 ; 415
Documento fuente:
Springer eBooks
Nota general:
Engineering (Springer-11647)
Contenido:
SOS Polynomials -- Optimization with SOS Polynomials -- Preliminaries of Nonlinear Systems -- Domain of Attraction in Polynomial Systems -- Domain of Attraction in Uncertain Polynomial Systems -- Domain of Attraction in Non-polynomial Systems -- Domain of Attraction via Multiple Lyapunov Function -- Miscellaneous
Restricciones de acceso:
Accesible sólo para usuarios de la UPV
Tipo recurso electrónico:
Recurso a texto completo
Detalles del sistema:
Forma de acceso: Web
ISBN:
9780857299598 978-0-85729-959-8
Entidades:
SpringerLink (Servicio en línea)
Enlace a formato físico adicional:
Printed edition: 9780857299581
Punto acceso adicional serie-Título:
Lecture Notes in Control and Information Sciences, 0170-8643 ; 415

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