Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems: adaptive fuzzy approach

Adaptive fuzzy-based tracking control designs are proposed in the paper for both holonomic mechanical systems as well as a large class of nonholonomic mechanical systems with plant uncertainties and external disturbances. A unified and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic mechanical control systems, respectively. First, a fuzzy logic system is introduced to learn the behavior of unknown (or uncertain) mechanical dynamics by using an adaptive algorithm. Next, the effect of approximation error on the tracking error must be efficiently eliminated by employing an additional robustifying algorithm. Consequently, hybrid adaptive-robust controllers can be constructed such that the resulting closed-loop mechanical systems guarantee a satisfactorily transient and asymptotic performance. Furthermore, a partitioned procedure with respect to the above developed adaptive fuzzy logic approximators is introduced such that the number of fuzzy IF-THEN rules is significantly reduced and the developed control schemes can be easily implemented from the viewpoint of practical applications. Finally, simulation examples are presented to illustrate the tracking performance of a two-link constrained robot manipulator and a vertical wheel rolling on a plane surface by the proposed adaptive fuzzy-based control algorithms.