Robust Adaptive Fuzzy Control of a Class of Uncertain Nonlinear Systems With Unstable Dynamics and Mismatched Disturbances

This paper studies the robust stabilization problem for a class of uncertain nonlinear systems with unstable zero dynamics. The considered zero dynamic is not assumed to be input-to-state practically stable and contains nonlinear uncertainties and mismatched external disturbances. A new robust adaptive fuzzy control method is developed by combining H-infinity theory with backstepping technique. First, an ideal C-1 virtual control function is designed, which can guarantee the zero dynamic asymptotically stable with a suboptimal H-infinity performance. Then, based on some non-negative functions and backstepping design, the actual controller is constructed for the overall system, which ensures that the tracking error for the ideal virtual control signal converges to a priori accuracy regardless of external disturbances. In this design, an auxiliary signal is introduced to overcome the difficulties from the unavailable virtual reference signal. By exploiting the implicit function theorem, the proposed design technique is directly applied to a special case, where the zero dynamic is partially linear. A two inverted pendulums is used to illustrate the application and effectiveness of the proposed design method.