Direct adaptive robust fuzzy control for nonlinear strict-feedback systems

Using backstepping method, a direct adaptive robust fuzzy control algorithm is proposed for a class of uncertain nonlinear strict-feedback systems in this paper. Fuzzy systems are utilized to approximate unknown parts of the desired control inputs. The key assumption is that the norms of the optimal approximation parameter vectors and the approximation errors are bounded, and the bounds are unknown. The proposed algorithm reduces on-line computation burden and improves the robust control performance of the system. It is proven that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero by choosing appropriately design parameter. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.