Adaptive robust tracking for uncertain system

We study in this paper a robust optimal target tracking problem for a class of uncertain linear systems, where all unknown parameters and disturbances are bounded by ellipsoids. We propose an adaptive robust control strategy with a learning feature such that the size of the uncertainty set is reduced successively during the time horizon by adopting a set membership-based estimation procedure. For each given updated uncertainty set, we compute a robust optimal control law by efficiently solving a corresponding second-order cone programming problem.