PI Adaptive Fuzzy Control With Large and Fast Disturbance Rejection for a Class of Uncertain Nonlinear Systems

Design of controllers for uncertain systems is inherently paradoxical. Adaptive control approaches claim to adapt system parameters against uncertainties, but only if these uncertainties change slowly enough. Alternatively, robust control methodologies claim to ensure system stability against uncertainties, but only if these uncertainties remain within known bounds. This is while, in reality, disturbances and uncertainties remain faithfully uncertain, i.e., may be both fast and large. In this paper, a PI-adaptive fuzzy control architecture for a class of uncertain nonlinear systems is proposed that aims to provide added robustness in the presence of large and fast but bounded uncertainties and disturbances. While the proposed approach requires the uncertainties to be bounded, it does not require this bound to be known. Lyapunov analysis is used to prove asymptotic stability of the proposed approach. Application of the proposed method to a second-order inverted pendulum system demonstrates the effectiveness of the proposed approach. Specifically, system responses to fast versus slow and large versus small disturbances are considered in the presented simulation studies.