Adaptive Robust Control without Knowing Bounds of Parameter Variations

A discontinuous projection based adaptive robust control (ARC) design is constructed for nonlinear systems transformable to the semi-strict feedback form without knowing the bounds of parameter variations and uncertain nonlinearities. Departing from the existing robust adaptive control schemes in which the unknown bounds are estimated on-line, the proposed ARC design only adapts actual physical parameters and uses a fixed design bound plus certain robust feedback to account for the possible destabilizing effect of on-line parameter adaptation. The resulting ARC controller achieves a prescribed transient performance and final tracking accuracy in general; the exponential convergence rate of the transient tracking error and the bound of the final tracking error can be adjusted via certain controller parameters in a known form. In addition, in the presence of parametric uncertainties only, if the true parameters fall within the design bound, asymptotic output tracking is achieved. Furthermore, by choosing the design bound appropriately, the controller also has a well-designed built-in anti-integration windup mechanism to alleviate the effect of control saturation. Extensive comparative simulation studies are carried out to illustrate the proposed ARC control strategy.