Set-membership identification based adaptive robust control of systems with unknown parameter bounds

In this paper, a hybrid control architecture is proposed for the adaptive robust control of a class of nonlinear systems with uncertain parameter variation ranges. Specifically, the standard set-membership description of uncertainty is adopted - the bounds of the structural approximation errors associated with the parametrized models are assumed to be known but the variation ranges of model parameters are not available or poorly known. To effectively control this class of systems, set-membership identification (SMI) is performed in discrete-time domain and a simple bound-shrinking algorithm is developed to obtain non-conservative real-time estimation of the regions where model parameters could actually be. The estimated parameter variation bounds are subsequently used to construct a continuous-time domain projection type parameter adaptation law with varying boundaries to achieve a controlled learning process. An adaptive robust control (ARC) algorithm is then synthesized to handle the effect of both parametric uncertainties and the model approximation error effectively. It is theoretically shown that in general the proposed approach achieves a guaranteed transient and steady-state output tracking performance. In addition, asymptotic output tracking can also be achieved when certain conditions hold.