Robust $L_{\bf 2}$-Gain Compensative Control for Direct-Adaptive Fuzzy-Control-System Design

In this study, an effective and systematical robust approach for adaptive fuzzy-control-system design is proposed. In the design, a compensative-control law is proposed to provide the finite
$L_2$
-gain property for direct-adaptive fuzzy-control systems to cope with possible external disturbances and approximation errors of the system. An integral term is further introduced into the compensative-control law to provide a more stable edge in order to have better control performance. With such a compensative-control law, the control performance can be anticipated in the
$L_2$
-gain robust-control sense. As a consequence, the dead-zone modification approach can then be employed to resolve the parameter-drift problem occurring in traditional learning of adaptive fuzzy-control systems. Finally, various simulations are conducted to demonstrate the effectiveness of the proposed approach.