Stable adaptive fuzzy control of nonlinear systems

The author develops a direct adaptive fuzzy controller which does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The specific formula of the bounds is provided so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin. Simulation results show that the direct adaptive fuzzy controller can perform successful control without using any fuzzy control rules. After incorporating some fuzzy control rules into the controllers the adaptation speed became much faster. The author also showed explicitly how the supervisory control forced the state to be within the constraint set and how the adaptive fuzzy controller learned to regain control