## Fuzzy adaptive control of multivariable nonlinear systems.(English)Zbl 0976.93049

The authors develop a robust fuzzy adaptive control scheme for a class of unknown nonlinear MIMO systems. The uncertainties are divided into two parts: A first type can be viewed as matched uncertainties, which are modeled by fuzzy systems and the design of fuzzy equivalence control. The second type can be treated as the unmatched uncertainties including modeling errors (fuzzy system approximation errors) and disturbances, etc., which cannot be modeled by fuzzy systems. Since the unmatched uncertainties may act as combined disturbance, it can lead to unstability of the closed-loop system, so a robust compensator is designed by the $$H^\infty$$ control technique to reject this kind of uncertainties. The whole adaptive control scheme not only guarantees uniform ultimate boundedness, but also makes the worst case effect on the tracking error due to the unmatched uncertainties to be less than or equal to a desired attenuation level.
Extensive simulations on the tracking control of a two-link rigid robotics manipulator verify the effectiveness of the proposed algorithms.

### MSC:

 93C42 Fuzzy control/observation systems 93C40 Adaptive control/observation systems 93B36 $$H^\infty$$-control 93C73 Perturbations in control/observation systems
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### References:

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