DSC-backstepping based robust adaptive fuzzy control for a class of strict-feedback nonlinear systems

A robust adaptive tracking control problem is discussed for a class of strict-feedback uncertain nonlinear systems. Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is developed to derive a novel robust adaptive tracking controller by use of the input-to-state stability (ISS) and by combining the dynamic surface control (DSC)-based backstepping technique and generalized small gain approach. The key features of the algorithm are that, firstly, the problem of ldquoexplosion of complexityrdquo inherent in the conventional backstepping method is circumvented, secondly, the number of parameters updated on line for each subsystem is reduced dramatically to 2. These features result in a much simpler algorithm, which is convenient to realize in application. In addition, it is shown that all closed-loop signals are semi-global uniformly ultimately bounded (SGUUB). Finally, simulation results via an application example of a pendulum system with motor is used to demonstrate the effectiveness and performance of the proposed scheme.