Stable adaptive control using fuzzy systems and neural networks

Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics. The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller. We prove that with or without such knowledge both adaptive schemes can "learn" how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input. In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation. The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane.