Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control

This paper presents a novel H∞ tracking-based direct adaptive fuzzy controller (HDAFC) for a class of perturbed uncertain affine nonlinear systems involving external disturbances and measurement noise. A practical interval type-2 (IT2) fuzzy logic system (FLS) is introduced to approximate the ideal control law. To eliminate the tradeoff between H∞ tracking performance and high gain at the control input, a modified output tracking error is introduced. Based on the proposed fired-rule-determination algorithm, a practical average defuzzifier expressed in parameterized and closed formula is developed for the IT2 FLS. Without the restriction that the control gain function is exactly known, the IT2 HDAFC is constructed and its adaptive law is derived by virtue of the Lyapunov synthesis. To improve control performance under measurement noise, the recursive linear smoothed Newton predictor is further introduced as a delayless output filter. Simulated application of a single-link robot manipulator demonstrates the superiority of the proposed approach over the previous approach in terms of the settling time, tracking accuracy, energy consumption and smoothness of the control input.

► We give a modified tracking error to eliminate the high control input gain.
► We remove the assumption that the control gain must be known.
► We give a practical average defuzzifier for the interval type-2 fuzzy logic system.