Robust adaptive fuzzy tracking control for a class of MIMO systems: A minimal-learning-parameters algorithm

A robust adaptive fuzzy tracking control problem is discussed for a class of uncertain MIMO nonlinear systems with strongly coupled interconnections. T-S fuzzy systems are used to approximate the unknown system uncertainties. Combining ldquodynamic surface control(DSC)rdquoapproach with ldquominimal learning parameters(MLP)rdquo algorithm, a systematic procedure for controller design is developed. The key features of the proposed scheme are that, firstly, the problem of ldquoexplosion of complexityrdquo inherent in the conventional backstepping method is circumvented, secondly, the number of parameters updated on line for each subsystem is reduced dramatically to 2, one for T-S fuzzy system and the other for the bound of disturbances, and, thirdly, the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is removed. These features result in a much simpler algorithm, which is easy to be implemented in application. It is shown that all the closed-loop signals are semi-globally uniformly ultimately bounded(SGUUB) based on Lyapunov theory. Finally, simulation results via a numerical example validate the effectiveness and performance of the proposed scheme.