Worst-case state estimation and simulation of uncertain discrete-time systems using zonotopes

In this paper a new approach for worst-case state estimation and simulation under structured uncertainty based on the use of an existent algorithm for solving validated initial value problems is introduced. Worst-case state simulation consists in computing a region of confidence for the system state, based on a deterministic uncertainty model for the system matrices and the previous confidence region for the system state. On the other hand, worst-case state estimation, also known, as set-membership state estimation consists in computing a region of confidence for the system state, based on a deterministic uncertainty model for the system matrices, the previous confidence region for the system state and the measures available considering also a deterministic model for the noise. The approach presented in this paper is intended for systems described by a discrete-time model with time varying parameters only known to belong to intervals. The algorithm formulates the problem of worst-case state estimation and simulation as a discrete initial value problem with bounded initial conditions that can be simulated using the Kuhn´s algorithm based on zonotopes. The proposed algorithm avoids one of the main problems of worst-case estimation and simulation, the problem on exponentially grow of uncertainty due to the wrapping effect with low computational cost.