Approximation-Free State-Feedback Backstepping Controller for Uncertain Pure-Feedback Nonautonomous Nonlinear Systems Based on Time-Derivative Estimator

A novel backstepping controller for uncertain single-input single-output pure-feedback nonaffine and nonautonomous nonlinear systems based on the time-derivative estimator (TDE) is proposed. Using TDEs, time-derivatives of error signals used in virtual control terms are directly estimated in every backstepping design steps. As a result, the control law has a relatively simple form. In addition, convergence of tracking error to a small neighborhood of origin is guaranteed regardless of unstructured uncertainties or unmatched disturbances in the controlled system. It does not require separate adaptive schemes or universal approximators such as neural networks or fuzzy logic systems adaptively tuned online to cope with system uncertainties. Simulation results demonstrated the simplicity and good performance of the proposed approximation-free controller.