TY - GEN
T1 - Observer design for a class of parabolic PDE via sliding modes and backstepping
AU - Miranda, Ramon
AU - Chairez, Isaac
AU - Moreno, Jaime
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77956602192&partnerID=8YFLogxK
U2 - 10.1109/VSS.2010.5544678
DO - 10.1109/VSS.2010.5544678
M3 - Contribución a la conferencia
AN - SCOPUS:77956602192
SN - 9781424458318
T3 - Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010
SP - 215
EP - 220
BT - Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010
T2 - 2010 11th International Workshop on Variable Structure Systems, VSS 2010
Y2 - 26 June 2010 through 28 June 2010
ER -