Fuzzy Controller Design IV: H∞ Strategy-Based Robust Approach

Abstract

In Chap. 4, we described the design of stable adaptive fuzzy controllers for the nonlinear plants employing Lyapunov theory-based adaptation rules. An additional supervisory control law was also utilized to ensure the boundedness of the states of the plants in course of tracking the reference signal. In addition to the stable design of the fuzzy controller, achieving the robust behavior is also a very important feature during the implementation of the plant in practice [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. In [1], the authors presented one of the earliest, most notable methodologies of designing H∞ tracking control-based robust adaptive fuzzy controllers. Here, matrix Riccati-like theorem had been utilized to ensure the attenuation of tracking error in the presence of external disturbances applied to the plant. Lyapunov theory had also been utilized to derive the adaptation law and robust control law additional to the fuzzy control law, obtained from a T-S-type fuzzy controller configuration. Thus, the stability and robustness, along with H∞ control-based tracking performance, were achieved for a class of nonlinear plants with external disturbances. In [2, 3], authors further showed the applicability of the H∞ tracking control-based robust adaptive fuzzy controllers with some other mathematical treatments, but the final formulation of the adaptive law and robust control action was identical with [1].