The Adaptive Control of Nonlinear Systems Using the T-S-K Fuzzy Logic

Fuzzy adaptive tracking controllers for a class of uncertain nonlinear dynamicalsystems are proposed and analyzed. The controller consists of adaptive and robustifyingcomponents whose role is to nullify the effect of uncertainties and achieve a desiredtracking performance. The interactions between the two components have beeninvestigated. We use the Takagi-Sugeno-Kang type of the fuzzy logic system to approximatethe controller. It is proved that the closed-loop system using this adaptive fuzzy controlleris globally stable in the sense that all signals involved are bounded. Finally, we apply themethod of direct adaptive fuzzy controllers to control an inverted pendulum and thesimulation results are included.