Adaptive fuzzy backstepping dynamic surface control of uncertain nonlinear systems based on filters

In this paper, a novel adaptive fuzzy backstepping output feedback control scheme is proposed for a class of single input single output (SISO) uncertain nonlinear systems without measurements of states. Fuzzy logic systems (FLS) are used to tackle unknown nonlinear functions, and the adaptive fuzzy output feedback controller is constructed by combining filters observer design and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the observer error and tracking error converge to a small neighborhood of origin. Three key advantages of our scheme are that (i) the proposed control method does not require that all the states of the system be measured directly, (ii) only one parameter needs to be updated online, and (iii) both problems of ”dimension curse” and ”explosion of complexity” are avoided. The computational burden has thus been greatly reduced. Finally, a simulation is included to illustrate the effectiveness of the proposed approach.