ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Geretti, Luca; Sandretto, Julien Alexandre Dit; Althoff, Matthias; Benet, Luis; Chapoutot, Alexandre; Chen, Xin; Collins, Pieter; Forets, Marcelo; Freire, Daniel; Immler, Fabian; Kochdumper, Niklas; Sanders, David P.; Schilling, Christian

doi:10.29007/zkf6

Cited by 14 publications

(18 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unique to our method, we can compute reachable states for black-box systems, as the Koopman linearization process uses data to create linear approximations in the space of observable functions. In the future we plan to further optimize the method, as well as to create a user-friendly tool in order to participate in the annual nonlinear reachability competition [25].…”

Section: Discussionmentioning

confidence: 99%

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

Bak¹,

Bogomolov²,

Duggirala³

et al. 2021

Preprint

View full text Add to dashboard Cite

Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we explore verification methods that leverage a connection between these two classes of systems based on the concept of the Koopman operator. The Koopman operator links the behaviors of a nonlinear system to a linear system embedded in a higher dimensional space, with an additional set of so-called observable variables. Although, the new dynamical system has linear differential equations, the set of initial states is defined with nonlinear constraints. For this reason, existing approaches for linear systems reachability cannot be used directly. In this paper, we propose the first reachability algorithm that deals with this unexplored type of reachability problem. Our evaluation examines several optimizations, and shows the proposed workflow is a promising avenue for verifying behaviors of nonlinear systems.

show abstract

Section: Discussionmentioning

confidence: 99%

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

Bak¹,

Bogomolov²,

Duggirala³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, linear systems can be embedded in algorithms to analyze nonlinear systems [17]. Further case studies and comparison with other state-of-the-art tools can be found in [2,19].…”

Section: Origin Of Lazysets and Current Applicationsmentioning

confidence: 99%

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

2021

JCON

View full text Add to dashboard Cite

LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. LazySets provides methods to apply common set operations, convert between different set representations, and efficiently compute with sets in high dimensions using specialized algorithms based on the set types. LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. While the library was originally designed for reachability and formal verification, its scope goes beyond such topics. LazySets is an easy-to-use, general-purpose and scalable library for computations that mix symbolics and numerics. In this article we showcase the basic functionality, highlighting some of the key design choices.

show abstract

“…Third, the number of variables can be large, for example 240 real-valued state variables in the 15-aircraft case. This complexity of system is beyond what is currently possible with nonlinear reachability tools [12], and even if it becomes possible, it is unlikely to run fast enough for use at runtime.…”

Section: Multi-aircraft Collision Avoidancementioning

confidence: 99%

The Black-Box Simplex Architecture for Runtime Assurance of Autonomous CPS

Mehmood,

Sheikhi,

Bak

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we explore using runtime verification to design safe cyber-physical systems (CPS). We build upon the Simplex Architecture, where control authority may switch from an unverified and potentially unsafe advanced controller to a backup baseline controller in order to maintain system safety. New to our approach, we remove the requirement that the baseline controller is statically verified. This is important as there are many types of powerful control techniques-model-predictive control, rapidly-exploring random trees and neural network controllersthat often work well in practice, but are difficult to statically prove correct, and therefore could not be used before as baseline controllers. We prove that, through more extensive runtime checks, such an approach can still guarantee safety. We call this approach the Black-Box Simplex Architecture, as both high-level controllers are treated as black boxes. We present case studies where model-predictive control provides safety for multi-robot coordination, and neural networks provably prevent collisions for groups of F-16 aircraft, despite occasionally outputting unsafe actions.

show abstract

ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Cited by 14 publications

References 22 publications

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

The Black-Box Simplex Architecture for Runtime Assurance of Autonomous CPS

Contact Info

Product

Resources

About