Fuzzy Adaptive Dynamic Surface Control with Constant Gain for Non-Affine Pure-Feedback Systems

This paper considers tracking control of non-affine pure-feedback systems with uncertain disturbances. The “explosion of complexity” in the process of backstepping design is eliminated by introducing the output of first-order filter to replace the derivative of virtual control signal. The mean-value theorem is utilized to overcome the non-affine difficulties appearing from the pure-feedback systems. By employing fuzzy logic systems (FLSs) and dynamic surface approach, an adaptive fuzzy controller with only one adaptive parameter is presented. Stability analysis shows that the proposed control method guarantees that all closed-loop system signals are semi-globally uniformly ultimately bounded. The main innovations of this paper are that the final gain function is viewed as an adjustable constant gain in the procedure of actual control signal design and the FLSs only handle state errors and disturbances. The new controller not only has the advantages of tracking performance, but it also reduces the computational burden in comparison with traditional adaptive backstepping method whose FLSs need to tackle with all gain function and system dynamics. A comparison simulation example shows the effectiveness of the proposed controller.