Related papers: Computing Distances between Reach Flowpipes
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…
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…
Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is…
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…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
Hypernetwork is a useful way to depict multiple connections between nodes, making it an ideal tool for representing complex relationships in network science. In recent years, there has been a marked increase in studies on hypernetworks,…
The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are…
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…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…