Stable adaptive control using fuzzy systems and neural networks

TLDR

The authors develop stable direct and indirect adaptive controllers based on Takagi‑Sugeno fuzzy systems, conventional fuzzy systems, or neural networks to achieve asymptotic tracking of a reference signal for continuous‑time nonlinear plants with poorly understood dynamics. The indirect scheme incorporates a priori knowledge of plant dynamics via exact equations or linguistic rules, while the direct scheme embeds such knowledge in the controller design, and a linguistic inverse‑dynamics technique is used to accelerate adaptation. The authors prove that both schemes learn to control the plant, keep internal signals bounded, and attain asymptotically stable tracking, as demonstrated by longitudinal control of an automobile in an automated lane.

Abstract

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.