000 04750nam a22004695i 4500
001 978-0-85729-959-8
003 DE-He213
005 20251006084447.0
007 cr nn 008mamaa
008 110829s2011 xxk| s |||| 0|eng d
020 _a9780857299598
020 _a99780857299598
024 7 _a10.1007/978-0-85729-959-8
_2doi
082 0 4 _a629.8
_223
100 1 _aChesi, Graziano.
_eauthor.
245 1 0 _aDomain of Attraction
_h[electronic resource] :
_bAnalysis and Control via SOS Programming /
_cby Graziano Chesi.
264 1 _aLondon :
_bSpringer London,
_c2011.
300 _aXVIII, 286p. 46 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Control and Information Sciences,
_x0170-8643 ;
_v415
505 0 _aSOS 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.
520 _aThe 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.
650 0 _aENGINEERING.
650 0 _aSYSTEMS THEORY.
650 0 _aPHYSICS.
650 1 4 _aENGINEERING.
650 2 4 _aCONTROL.
650 2 4 _aSYSTEMS THEORY, CONTROL.
650 2 4 _aNONLINEAR DYNAMICS.
650 2 4 _aCOMPLEXITY.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780857299581
830 0 _aLecture Notes in Control and Information Sciences,
_x0170-8643 ;
_v415
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-85729-959-8
_zVer el texto completo en las instalaciones del CICY
912 _aZDB-2-ENG
942 _2ddc
_cER
999 _c60180
_d60180