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

• Published in: ECC : 2001 European Control Conference : 4-7 September 2001 pp. 1691 - 1697
• Main Authors: Puig, V., Cuguero, P., Quevedo, J.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.09.2001
• Subjects: Algorithms; Bounded Uncertainty and Errors in Variables; Computation; Computational efficiency; Computational modeling; Computer simulation; Confidence; Estimation; Initial value problems; Mathematical model; Mathematical models; Observers; Orbits; Set-membership Estimation and Identification; Signal and Systems; State estimation; Uncertainty; Wrapping
• ISBN: 9783952417362; 395241736X
• DOI: 10.23919/ECC.2001.7076164

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.