Novel direct adaptive fuzzy control system design

In our earlier study, the property of L
₂
-gain robust control is incorporated into the direct adaptive fuzzy control design with the use of the compensative controller. The tracking control performance is guaranteed. In the study, we further employ the L
₂
-gain property to improve the adaptive law design. Due to the L
₂
-gain control property, the approximate error of the fuzzy system is estimable, and thus, an adaptive law with the approximate error feedback is proposed in the study. The novel adaptive law improves the learning speed so that the learning performances can be better. Since the L
₂
-gain based compensative controller can guarantee the tracking control performance and remove the effect of the gain function in the adaptive law. The direct adaptive fuzzy control system design of the paper not only has the satisfactory tracking control performance but also has the better learning performance. Various simulations are conducted to demonstrate the effectiveness of the proposed design.