# New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

Dalil Ichalal; Benoît Marx; José Ragot; Didier Maquin

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 1, page 197-210
- ISSN: 1641-876X

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topDalil Ichalal, et al. "New fault tolerant control strategies for nonlinear Takagi-Sugeno systems." International Journal of Applied Mathematics and Computer Science 22.1 (2012): 197-210. <http://eudml.org/doc/208095>.

@article{DalilIchalal2012,

abstract = {New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.},

author = {Dalil Ichalal, Benoît Marx, José Ragot, Didier Maquin},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Takagi-Sugeno model; fault tolerant control; simultaneous fault and state estimations; Polya's theorem; Lyapunov theory; input-to-state stability; adaptive fast state and fault observer (AFSFO); proportional-integral observer (PIO)},

language = {eng},

number = {1},

pages = {197-210},

title = {New fault tolerant control strategies for nonlinear Takagi-Sugeno systems},

url = {http://eudml.org/doc/208095},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Dalil Ichalal

AU - Benoît Marx

AU - José Ragot

AU - Didier Maquin

TI - New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 1

SP - 197

EP - 210

AB - New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.

LA - eng

KW - Takagi-Sugeno model; fault tolerant control; simultaneous fault and state estimations; Polya's theorem; Lyapunov theory; input-to-state stability; adaptive fast state and fault observer (AFSFO); proportional-integral observer (PIO)

UR - http://eudml.org/doc/208095

ER -

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## Citations in EuDML Documents

top- Ali Ben Brahim, Slim Dhahri, Fayçal Ben Hmida, Anis Sellami, An ${H}_{\infty}$ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults
- Rodolfo Orjuela, Benoît Marx, José Ragot, Didier Maquin, Nonlinear system identification using heterogeneous multiple models
- Hoda Moodi, Mohammad Farrokhi, Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent
- Marcin Mrugalski, An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection

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