Indirect adaptive robust control of nonstrict feedback nonlinear systems by a fuzzy approximation strategy

To solve the control problem of nonstrict feedback nonlinear systems, a backstepping technique based controller design method is developed by integrating a robust control law with the excellent parameter identification algorithm of indirect adaptive framework. Each of unknown system functions that contain whole states is approximated by adding together a bounded time-varying parameter and a fuzzy approximator related to the current step and previous states only in the backstepping design procedure, which solves the algebraic loop problem existing in nonstrict feedback systems. Then the command filter is combined with the adaptive backstepping to construct the robust control law by which the differentiation operation of the virtual control signal can be avoided. Subsequently the swapping scheme is used to convert the studied system into a linear time-varying form. Both the weight vector of the fuzzy logic system and the bounded time-varying parameter are estimated by a least-squares identification algorithm under relaxed excitation conditions, so that the accurate value of system functions can be obtained. All signals in the closed-loop system are proved to be bounded. A simulation example is put forward to verify effectiveness of the presented method.