A Novel and Efficient Order Reduction for Both Constrained Convex Generators and Constrained Zonotopes

A central challenge with any reachability technique is the growth over time of the data structures that store the set-valued estimates. There are various techniques established for constrained zonotopes (CZs), although their computational complexity represents a limiting factor on the size of the set descriptions when running the methods in real time. Thus, when running a guaranteed state observer to estimate the state of a dynamical system using CZs, the number of generators and constraints has to be maintained small such that the order reduction procedures can be run within the sampling time. This article resorts to using ellipsoids for portions of the set description, which results in a computationally efficient method for a particular class of constrained convex generators that can also be used for ellipsotopes and CZs. Our approach is shown to have comparable performance and in some cases outperforms existing methods for CZs. We provide numerical examples to illustrate the advantages of our proposed approach, particularly in the context of guaranteed state estimation.