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A stable self-structuring adaptive fuzzy control scheme for continuous single-input single-output nonlinear systems


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Phan, PA 2009 , 'A stable self-structuring adaptive fuzzy control scheme for continuous single-input single-output nonlinear systems', PhD thesis, University of Tasmania.

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Adaptive fuzzy control has been an active research area in the past decade.
Fundamental issues such as stability, robustness, and performance analysis have been
solved. However, one main drawback is the generally fixed structure of the fuzzy
controllers, which are normally chosen by trial-and-error in practice. Few attempts to
develop self-structuring AFC have been reported, and important issues such as
stability, computational efficiency, and implementability have not been investigated
thoroughly. In particular, the stability of the system when the structure changes has
not been proven. Thus, a more effective self-structuring AFC scheme is desirable.
The main objective of the research is to develop a stable self-structuring AFC
scheme for continuous-time single-input-single-output (SISO) uncertain nonlinear
A novel online self-structuring adaptive fuzzy control scheme that is applicable
for a number of classes of continuous SISO nonlinear systems is proposed. The
applicable classes include affine nonlinear systems, non-affine nonlinear systems, and
nonlinear systems in triangular forms. The main features of the proposed control
scheme are:
• It needs less restriction on the controlled plants and no restriction on the
design parameters.
• It employs a modified adaptive law that guarantees explicit boundedness of
adaptive parameters and control action.
• The self-structuring algorithm is relatively simple and guarantees explicit
boundedness of the number of rules generated.
• Only triangular membership functions are generated and only 2
membership functions are allowed to overlap to increase the
interpretability of generated fuzzy controllers.
• High-gain observers are used when not all the states are measurable and
the design of observers is completely separated from the design of
• For nonlinear systems in triangular forms, only one fuzzy system is needed
(unlike the back-stepping approach where one fuzzy system is needed at
each step).
• An approximation error estimator and an automatic switching mechanism
can be used to further increase the robustness and computational
The stability of the overall system, especially when the structure changes, is
guaranteed using the Lyapunov stability technique. The overall system is stable in the
sense that all the variables are bounded (including number of rules generated) and the
tracking error is uniformly ultimately bounded. The proposed control algorithms are
implemented in Matlab and Simulink for ease of simulation and practical application.
Numerous simulation examples are performed to demonstrate the theoretical results.
The proposed control scheme makes practical application of AFC easier.
Designers need to specify only a few design parameters and no longer have to specify
the controller structure by trial and error. A simulation or application can be quickly
and easily implemented using the developed controllers in Simulink.

Item Type: Thesis - PhD
Authors/Creators:Phan, PA
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