Lyapunov-function-based design of fuzzy logic controllers and itsapplication on combining controllers
Wong, L.K.; Leung, F.H.F.; Tam, P.K.S.
Industrial Electronics, IEEE Transactions on
Volume 45, Issue 3, Jun 1998 Page(s):502 - 509
Digital Object Identifier 10.1109/41.679009
Summary:This paper presents the design of fuzzy logic controllers (FLCs)
for nonlinear systems with guaranteed closed-loop stability and its
application on combining controllers. The design is based on heuristic
fuzzy rules. Although each rule in the FLC refers to a stable
closed-loop subsystem, the overall system stability cannot be guaranteed
when all these rules are applied together. In this paper, it is proved
that if each subsystem is stable in the sense of Lyapunov (ISL) under a
common Lyapunov function, the overall system is also stable ISL. Since
no fuzzy plant model is involved, the number of subsystems generated is
relatively small, and the common Lyapunov function can be found more
easily. To probe further, an application of this design approach to an
inverted pendulum system that combines a sliding-mode controller (SMC)
and a state feedback controller (SFC) is reported. Each rule in this FLC
has an SMC or an SFC in the consequent part. The role of the FLC is to
schedule the final control under different antecedents. The stability of
the whole system is guaranteed by the proposed design approach. More
importantly, the controller thus designed can keep the advantages and
remove the disadvantages of the two conventional controllers
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