Related papers: Sparse Polynomial Zonotopes: A Novel Set Represent…

The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…

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…

Aggregations of flexible loads can provide several power system services through demand response programs, for example load shifting and curtailment. The capabilities of demand response should therefore be represented in system operators'…

Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…

In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional…

We introduce the M-representation of polytopes, which makes it possible to compute linear transformations, convex hulls, and Minkowski sums with linear complexity in the dimension of the polytopes. When the polytope is a convex hull of a…

Polynomial zonotopes, a non-convex set representation, have a wide range of applications from real-time motion planning and control in robotics, to reachability analysis of nonlinear systems and safety shielding in reinforcement learning.…

We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…

Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is…

This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid…

Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective…

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)…

We present randomized algorithms to compute the sumset (Minkowski sum) of two integer sets, and to multiply two univariate integer polynomials given by sparse representations. Our algorithm for sumset has cost softly linear in the combined…

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…

In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on…

This paper proposes novel set-theoretic approaches for state estimation in bounded-error discrete-time nonlinear systems, subject to nonlinear observations/constraints. By transforming the polytopic sets that are characterized as zonotope…

We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather…

Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, based on a new concept of mixed sets defined as function images of symbol type domains, a compositional…

Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires…