In this letter, stable direct and indirect adaptive controllers are present
ed that use Takagi-Sugeno (T-S) fuzzy systems, conventional fuzzy systems,
or a class of neural networks to provide asymptotic tracking of a reference
signal vector for a class of continuous time multi-input multi-output (MIM
O) square nonlinear plants with poorly understood dynamics. The direct adap
tive scheme allows for the inclusion of a priori knowledge about the contro
l input in terms of exact mathematical equations or linguistics, while the
indirect adaptive controller permits the explicit use of equations to repre
sent portions of the plant dynamics. We prove that with or without such kno
wledge the adaptive schemes can "learn" how to control the plant, provide f
or bounded internal signals, and achieve asymptotically stable tracking of
the reference inputs. We do not impose any initialization conditions on the
controllers and guarantee convergence of the tracking error to zero.