Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.