It can be seen that each individual

It can be seen that each individual approach like SMC, NN or DO has their own advantages and disadvantages, as pointed out in the aforementioned discussion. Therefore, the performance of the system might be reduced when applying the techniques individually into the practical applications. In order to enhance performance of the system, hybrid control methods, which combine the advantages while trying to eliminate the disadvantages of the individual components, have been developed. For example, due to the advantages of the ISMC and DO, a hybrid ISMC and DO has been developed in [43]–[45]. Hybrid approximation and estimation methods based on NN/FLS and DO have also been developed in [46]–[52]. On the other hand, due to the robustness property of the SMC and the approximation capability of NN/fuzzy logic, some hybrid controllers, which combine the merits of both parties, have been developed [53]–[56]. However, as aforementioned discussions, since the ISMC offers some major advantages over the SMC, it is desired to develop a hybrid controller, which can combine the merits of the ISMC and the NN/FLS. Unfortunately, very few efforts in the literature have been spent to realize this interesting control paradigm [57]. The reason may come from the fact that it is difficult to reconstruct the control input of the hybrid system such that the stability and convergence of the whole system can be guaranteed. In addition, in order to promote the system performance, it is desired that the system should take the advantages of the ISMC, learning technique and DO into account. This demand is particularly needed for the FTC system, where strong unknown nonlinear functions (uncertainty, disturbance and fault) are present and high robustness controller is required. This is one of the most motivations of this paper.