Reachability Analysis of Linear Hybrid Systems via Block Decomposition

Bogomolov, Sergiy; Forets, Marcelo; Frehse, Goran; Potomkin, Kostiantyn; Schilling, Christian

doi:10.1109/tcad.2020.3012859

“…LazySets has also been applied to the challenging domain of hybrid systems (systems with mixed discrete-continuous dynamics) for set propagation [9] and synthesis [32]. Such problems require switching between different set representations and handling intersections efficiently and accurately.…”

Section: Origin Of Lazysets and Current Applicationsmentioning

confidence: 99%

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

2021

JCON

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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.

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“…Further case studies and comparison with other state-of-the-art tools can be found in [2,15]. LazySets has also been applied to the challenging domain of hybrid systems (systems with mixed discrete-continuous dynamics) for set propagation [8] and synthesis [25]. Such problems require switching between different set representations and handling intersections efficiently and accurately.…”

Section: Origin Of Lazysets and Current Applicationsmentioning

confidence: 99%

LazySets.jl: Scalable Symbolic-Numeric Set Computations

Forets,

Schilling

2021

Preprint

Self Cite

0

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

“…This linear system can be computed either symbolically from differential equations or-importantly for black-box systems-from data derived from real-world system executions or simulations [39]. For reachability analysis, such a method is promising, as there exist highly-scalable methods to compute reachable sets for linear systems [27,41,8,11]. However, directly applying existing algorithms is not possible, as the observable variables are nonlinear functions of the original state variables.…”

Section: Introductionmentioning

confidence: 99%

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

Bak¹,

Bogomolov²,

Duggirala³

et al. 2021

Preprint

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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.

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Reachability Analysis of Linear Hybrid Systems via Block Decomposition

Cited by 9 publications

References 38 publications

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

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

LazySets.jl: Scalable Symbolic-Numeric Set Computations

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

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