Ellipsoidal state estimation for dynamical systems

The ellipsoidal estimation of state for dynamical systems is an efficient technique for the set-membership modelling of uncertain dynamical systems. In the paper, an overview of recent results on the method of ellipsoids for the approximation of reachable sets of dynamical systems is presented. Optimal ellipsoidal estimates of reachable sets are considered for various optimality criteria, including the new one equal to the projection of an ellipsoidal onto a given direction. Nonlinear differential equations governing the evolution of ellipsoids are analyzed and simplified. The method of ellipsoids is extended to the case where the parameters of the system are uncertain and/or subjected to unknown but bounded perturbations. Generalizations of the method of ellipsoids and its applications to control problems for dynamical systems are discussed.