H∞ tracking-based adaptive fuzzy sliding mode controller design for nonlinear systems

Abstract

An H∞ tracking-based adaptive fuzzy sliding mode controller (H∞ AFSMC) is proposed for a class of nonlinear systems involving system uncertainties and external disturbances. The H∞ tracking control design method and the adaptive fuzzy sliding mode control technique are combined in the design of the H∞ AFSMC controller. By the Lyapunov theory, it is shown that the proposed controller has the following advantages: it can inhibit the chattering phenomenon and can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Subsequently, the problem of H∞ AFSMC design is characterised in terms of an eigenvalue problem, which can be efficiently solved by using convex optimisation techniques. Finally, an inverted pendulum system is simulated to demonstrate the validity and effectiveness of the proposed controller.