Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem: Recent Study

Practical nonlinear systems can usually be represented by partly linearizable models with unknown
nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive
fuzzy robust control (AFRC) algorithm for such systems. The AFRC effectively combines techniques
of adaptive control and fuzzy control and it improves the performance by retaining the advantages of
both methods. The linearizable part will be linearly parameterized with unknown but constant
parameters, and the discontinuous-projection-based adaptive control law is used to compensate
these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities.
Robust control law ensures the robustness of closed-loop control system. A systematic design
procedure of the AFRC algorithm by combining the back stepping technique and small-gain approach
is presented. Then the closed-loop stability is studied by using small gain theorem and the result
indicates that the closed-loop system is semi-globally uniformly ultimately bounded.