Related papers: Sparse Spectrahedral Shadows for State Estimation …

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…

Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in…

A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal-Sottile-Sturmfels (2011). We study this class…

Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…

Spectrahedral shadows are projections of linear sections of the cone of positive semidefinite matrices. We characterize the polynomials that vanish on the boundaries of these convex sets when both the section and the projection are generic.

This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to…

We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…

Polyhedra and spectrahedra over the real numbers, or more generally their images under linear maps, are respectively the feasible sets of linear and semidefinite programming, and form the family of semidefinite-representable sets. This…

Symmetric objects are common in daily life and industry, yet their inherent orientation ambiguities that impede the training of deep learning networks for pose estimation are rarely discussed in the literature. To cope with these…

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly…

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation…

The intersection of an affine subspace with the cone of positive semidefinite matrices is called a spectrahedron. An orthogonal projection thereof is called a spectrahedral shadow or projected spectrahedron. Spectrahedra and their…

This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems with bounded uncertainties. The novel method builds upon essential properties and computational advantages of constrained zonotopes (CZs)…

Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…

This article is concerned with the problem of approximating a not necessarily bounded spectrahedral shadow, a certain convex set, by polyhedra. By identifying the set with its homogenization the problem is reduced to the approximation of a…

This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear…

Unlike many urban localization methods that return point-valued estimates, a set-valued representation enables robustness by ensuring that a continuum of possible positions obeys safety constraints. One strategy with the potential for…

We study the structure of the set of algebraic curvature operators satisfying a sectional curvature bound under the light of the emerging field of Convex Algebraic Geometry. More precisely, we determine in which dimensions $n$ this convex…

Recent advances show that semi-supervised implicit representation learning can be achieved through physical constraints like Eikonal equations. However, this scheme has not yet been successfully used for LiDAR point cloud data, due to its…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…