An adaptive control scheme for discrete-time T-S fuzzy systems with unknown membership parameters

This paper presents a new study of adaptive control of discrete-time input-output multiple-delay T-S fuzzy systems whose membership function parameters and dynamics parameters are both unknown. A multiple-delay prediction fuzzy system model with such uncertain parameters is used to form a nonlinearly parametrized estimation error. A gradient algorithm is derived, based on a nonlinear error model, to adaptively update the parameters of the feedback control law for the uncertain T-S fuzzy system. Stability and robustness of the adaptive laws are analyzed in the T-S system model framework to clarify the inherent system properties and specify the key design conditions as well. Simulation results are presented to illustrate the adaptive control design and verify the desired closed-loop system properties.