High gain control of Stochastic Differential Equations: Analytical and Numerical methods for the calculation of moment exponents and rotation numbers - Couverture souple

Matsikis, Iakovos

 
9783838366531: High gain control of Stochastic Differential Equations: Analytical and Numerical methods for the calculation of moment exponents and rotation numbers
Couverture souple
ISBN 10 : 3838366530 ISBN 13 : 9783838366531
Editeur : LAP LAMBERT Academic Publishing, 2010

Synopsis

This work tries to address the problem of assessing the long term dynamics of control systems described by linear, stochastic, differential equations upon application of high gain, proportional, output feedback. Stability of such stochastic systems is characterized by moment exponents and rotation numbers. We present two analytical techniques to determine mean or else almost sure stability and rotation in state space. The first is projection onto the unit sphere, derivation of the associated Fokker-Planck equation on projective space and finally computation of mean exponents and rotation numbers, the stochastic equivalents of the real and imaginary parts of eigenvalues, by using ergodic arguments that allow passing from time to space averages. The second is an expansion technique based on a perturbation analysis of the generator that defines the diffusion. As an alternative or compliment to mean stability we discuss furthermore second mean stabilization and a linear algebraic technique with roots in control theory for calculating second mean exponents.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This work tries to address the problem of assessing the long term dynamics of control systems described by linear, stochastic, differential equations upon application of high gain, proportional, output feedback. Stability of such stochastic systems is characterized by moment exponents and rotation numbers. We present two analytical techniques to determine mean or else almost sure stability and rotation in state space. The first is projection onto the unit sphere, derivation of the associated Fokker-Planck equation on projective space and finally computation of mean exponents and rotation numbers, the stochastic equivalents of the real and imaginary parts of eigenvalues, by using ergodic arguments that allow passing from time to space averages. The second is an expansion technique based on a perturbation analysis of the generator that defines the diffusion. As an alternative or compliment to mean stability we discuss furthermore second mean stabilization and a linear algebraic technique with roots in control theory for calculating second mean exponents.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
3838366530
ISBN 13 
9783838366531
Reliure
Broché
Nombre de pages
156
Coordonnées du fabricant
non disponible
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