Zonotope Order Reduction in Robust Estimation

Zonotopes are symmetric polytopes that are widespread in reachability analysis, fault detection, hybrid systems, and robust estimation and control. In these applications, recursive computations with zonotopes increase the complexity of the zonotopes (order of the zonotopes) along with the computational cost. Therefore, a zonotope order reduction is necessary for real-time applicability. In this paper, a new zonotope order reduction method is proposed. The new method is based on the combination of principal component analysis (PCA) and the Gram-Schmidt orthogonalization. The method is tested under two different zonotopic state estimation approaches. Results show that the performance of the proposed method is better with respect to the volume of the reduced zonotope.