Adaptive fuzzy sliding controller design with approximate error feedback

The research about sliding based approaches is a widely studied topic to the adaptive fuzzy control system designs. In this paper, a novel state error feedback sliding controller is proposed. An optimal feedback gain is required and in this study it is assumed to be unknown. Usually, a rudimentary feedback gain is used. Besides, in order to approximate the state error feedback sliding controller with the optimal feedback gain, an adaptive fuzzy system is employed. Thus, the proposed control scheme consists of an adaptive fuzzy system and a state error feedback sliding controller with a rudimentary feedback gain. In the system framework, the rudimentary state error feedback sliding controller can be viewed as the approximate error estimator of the adaptive fuzzy system. Therefore, such an estimated error can be fed back to the learning of the fuzzy system through a modified adaptive law. With such an approximate error feedback, it is clearly evident from our simulation that the learning speed of the proposed learning scheme is faster than that of the original scheme. Also, with the proposed controller, the system stability not only is guaranteed, but also becomes more stable.