Reference:
Zs. Lendek,
J. Lauber,
T.M. Guerra,
R. Babuska, and
B. De Schutter,
"Adaptive observers for TS fuzzy systems with unknown polynomial
inputs," Fuzzy Sets and Systems, vol. 161, no. 15, pp.
2043-2065, Aug. 2010.
Abstract:
A large class of nonlinear systems can be well approximated by
Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents.
However, in practical applications, the process under consideration
may be affected by unknown inputs, such as disturbances, faults or
unmodeled dynamics. In this paper, we consider the problem of
simultaneously estimating the state and unknown inputs in TS systems.
The inputs considered in this paper are 1) polynomials in time (such
as a bias in the model or an unknown ramp input acting on the model)
and 2) unmodeled dynamics. The proposed observer is designed based on
the known part of the fuzzy model. Conditions on the asymptotic
convergence of the observer are presented and the design guarantees an
ultimate bound on the error signal. The results are illustrated on a
simulation example.