Parameterization and Adaptive Control of Multivariable Noncanonical T--S Fuzzy Systems

This paper conducts a new study for adaptive Takagi–Sugeno (T–S) fuzzy approximation-based control of multi-input and multi-output (MIMO) noncanonical-form nonlinear systems. Canonical-form nonlinear systems have explicit relative degree structures, whose approximation models can be directly used to derive desired parameterized controllers. Noncanonical-form nonlinear systems usually do not have such a feature, nor do their approximation models, which are also in noncanonical forms. This paper shows that it is desirable to reparameterize noncanonical-form T–S fuzzy system models with smooth membership functions for adaptive control, and such system reparameterization can be realized using relative degrees, a concept yet to be studied for MIMO noncanonical-form T–S fuzzy systems. This paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters, by first deriving various relative degree structures and normal forms for such systems. Then, a reparameterization procedure is developed for such system models, based on which adaptive control designs are derived, with desired stability and tracking properties analyzed. A detailed example is presented with simulation results to show the new control design procedure and desired control system performance.