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A geometric approach to nonlinear fault detection and isolation. (English) Zbl 1009.93003
The dual concepts of unobservability distributions and observability codistributions proved to be very useful to deal with problems of fault detection in linear control systems with disturbances. This paper extends an approach used for linear systems to the class of control-affine (nonlinear with respect to state) systems. The problem of fault detection and isolation is formulated and reduced to the so-called “fundamental problem of residual generation” (FPRG). In the linear case it is known that the FPRG has a solution if and only if the intersection of a certain unobservability distribution with the fault distribution is trivial. In this paper it is shown that, under appropriate regularity and technical assumptions, an analogous condition is necessary in order for the FPRG to have a solution. This condition is more conveniently formulated in a dual form, i.e., in terms of an observability codistribution. Conversely, it is shown that if the nonlinear analogous (dual) to the unobservability condition holds then there exists a weakly observable “quotient” system that is very useful in the design of a residual generator for the fault detection problem.
MSC:
93B07Observability
93B29Differential-geometric methods in systems theory (MSC2000)
93B51Design techniques in systems theory
93C10Nonlinear control systems