Related papers: Reachability Analysis for Linear Systems with Unce…
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 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,…
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 paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to…
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…
This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
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.…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…