Computing the allowable uncertainty of sparse control configurations

Abstract

Given a generic Control Configuration Selection (CCS) protocol and a plant uncertainty description isomorph to a unit ball in a finite-dimensional Lp space, we search for the largest perturbation radius for which the nominal configuration remains the preferred one. To this aim, we develop a randomized search algorithm based on sampling the uncertain plants and characterize its statistical performance. By adopting an intuitive accuracy measure that relates to the volume of points in which the preferred configuration differs from the nominal one, we devise a generally applicable strategy that allows for arbitrarily accurate estimates, in a specific probabilistic sense, depending on the number of uncertain plants that are sampled. We benchmark the proposed algorithm using examples from the literature and in a data center flow provisioning problem. In the latter setting, we identify the uncertainty description with the space of controls and sample the “uncertain” plants from an underlying nonlinear model.