Robust adaptive fuzzy control of nonaffine systems guaranteeing transient and steady state error bounds

Abstract

We consider the tracking problem of Single Input Single Output, unknown, nonaffine systems with guaranteed prescribed performance in the presence of additive input disturbances. By prescribed performance we mean that the tracking error should converge to a predefined arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small preassigned constant. An output error transformation is incorporated to produce a transformed system the boundedness of which is proven to be sufficient to solve the problem. A fuzzy system is utilized to approximate the unknown system nonlinearities and consequently a smooth robust adaptive fuzzy controller is designed to achieve the boundedness of the transformed system as well as of all signals in the closed loop. System performance is independent of controller gains, while no almost perfect fuzzy modeling is required. Simulation studies clarify and verify the approach.