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New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

Ichalal D., Marx B., Ragot J., Maquin D.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 1

197-210

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.

Dynamika układów hybrydowych

Czornik A.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

2008

z. 151

31-36

Badanie dynamiki układów hybrydowych jest źródłem wielu interesujących i trudnych problemów matematycznych. Celem tej pracy jest zreferowanie postępów w badaniach własności dynamiki układów hybrydowych ze szczególnym uwzględnieniem problemu stabilności. Z problemem stabilności ściśle związane są problemy eksponencjalnego wzrostu i twierdzenia odwrotne do twierdzenia Lapunowa. Oba te zagadnienia zostaną zreferowane. W pracy zostanie zasygnalizowanych również kilka otwartych problemów.

The study of the hybrid systems dynamics gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to review progress made in research of hybrid systems dynamics. We concentrate our attention on stability. Closely related to the concept of stability are the notations of exponential growth and converse Lyapunov theorems, both of which are discussed. We also point out some problems that remain open.