Fuzzy sliding mode control of Lorenz chaotic system using improved model reference approach

In this paper, by combining the merits of model reference adaptive control, sliding mode and fuzzy control a novel control approach is proposed to address the stabilization and tracking problem of Lorenz chaotic system without chattering phenomenon in the face of structure and unstructured uncertainties. In this control scheme an adaptive fuzzy system is used to estimation unknown function. As a result, there is no need to calculate the bound of unknown function and chattering phenomenon is attenuated. One of the advantages of proposed method is that the behavior of close loop system is similar to proposed model reference in the presence of uncertainties and disturbances. As a result, the shortcoming of adaptive control in the presence of unmodeled dynamics and external disturbances is compensated. Another advantage of proposed approach is that chaotic systems have unpredictable behavior and extreme sensitivity to initial conditions. The stability analysis is verified and the effectiveness of the proposed method is compared with backstepping method through simulation. Numerical simulations illustrate that proposed control approach is superior to backstepping method already published in literatures in overcoming uncertainties.