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Título del libro: Proceedings Of The 2010 11th International Workshop On Variable Structure Systems, Vss 2010
Título del capítulo: Observer design for a class of parabolic PDE via sliding modes and backstepping

Autores UNAM:
JAIME ALBERTO MORENO PEREZ;
Autores externos:

Idioma:
Inglés
Año de publicación:
2010
Palabras clave:

Error dynamics; Explicit solutions; Exponential convergence; Exponentially stable; Hyperbolic PDEs; Integral transformations; Lyapunov theories; Numerical example; Observer design; Observer gain; Output injection; Parabolic PDEs; Research fields; Sliding modes; Target systems; Theoretical result; Volterra; Aircraft engines; Differential equations; Hyperbolic functions; Integral equations; Backstepping


Resumen:

Observation problem for systems governed by Partial Differential Equations (PDE) has been a research field of its own for a long time. In this paper it is presented an observer design for a class or parabolic PDE's using sliding modes theory and bacstepping-like procedure in order to achieve exponential convergence. A Volterra-like integral transformation is used to change the coordinates of the error dynamics into exponentially stable target systems using the backstepping-like procedure. This gives as a result the output injection functions of the observer which are obtained by solving a hyperbolic PDE system. Sliding modes are used to find an explicit solution to the hyperbolic PDE system and to make the observer gains to be discontinuous which have well known advantages. Theoretical results were proved using the Lyapunov theory. A numerical example demonstrates the proposed method effectiveness. © 2010 IEEE.


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