Differential Flatness Theory-Based Adaptive Fuzzy Control of Underactuated Nonlinear Systems

摘要

An adaptive fuzzy controller is designed for a class of underactuated nonlinear robotic manipulators, under the constraint that the system's model is unknown. The control algorithm aims at satisfying the H_∞ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the robotic system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system's parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in H_∞ tracking performance. The efficiency of the proposed adaptive fuzzy control scheme is checked in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.