Paper Critique
While reachability analysis is needed for verification and synthesis of hybrid systems, computing
reachable sets is computationally very expensive. In particular, for high dimensional systems,
computing exact reachable sets can be impossible. This paper tries to alleviate this problem by
offering an alternative representation for the reachable sets which is a high-quality
approximation of the exact sets and allows efficient computation.
In this paper, they only consider “uncertain linear systems” of a certain form which serves as a
special case of general linear systems. Then, they show that over-approximating reachable sets
as zonotopes allows for efficient computation and high-quality approximations. The use of
zonotopes is motivated by closure properties of zonotopes which also allows for efficient
computation of operations like linear transformations and Minkowski sums over zonotopes.
The paper does a good job of explaining the preliminaries for the work. The experiments show
promising results. Also, the paper annotates the computational complexity of various
operations and approaches, making it easier to see how this approach is computationally
compelling.
However, it is not clear to me how representative of the real-world tasks are the experiments.
Also, as briefly mentioned in the paper as well, the reduction step is very heuristic based and
the results of different design choices are not well studied. The paper has also well identified
the immediate extensions to this work, namely, more general classes of linear-systems and nonlinear systems.