Set Propagation Techniques for Reachability Analysis

Althoff, Matthias; Frehse, Goran; Girard, Antoine

doi:10.1146/annurev-control-071420-081941

Cited by 140 publications

(76 citation statements)

References 133 publications

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“…As an illustrative example, suppose that we are interested in the formula Ω 0 = CH (X 0 , ΦX 0 ⊕ Y ), where CH and ⊕ are defined in Table 1, X 0 and Y are sets, and Φ is a matrix defined in Appendix C.1. Such formulas are prevalent in reachability analysis of linear initial-value problems, or nonlinear ones after some form of conservative linearization; see for example [3,16] and references therein. Given the sets X 0 , Y , and the matrix Φ, we can write: § ¤…”

Section: Type Compositionmentioning

confidence: 99%

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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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Section: Type Compositionmentioning

confidence: 99%

“…In the first benchmark we evaluate the support function on the lazy set. 3 In the second benchmark we first convert to a concrete set representation (in this case a polygon in vertex representation) and then evaluate the support function. The first case is two orders of magnitude faster.…”

Section: Support-function Calculusmentioning

confidence: 99%

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

2021

JCON

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“…There is a huge body of work on formal verification of continuous and hybrid systems, based on reachability checking [4], computation of invariants [36,41], deductive methods [34,35,47], and so on. In particular, KeYmaera X [18] provides a user interface for verifying hybrid systems using differential dynamic logic, with automatic generation of proofs checkable in Isabelle [9].…”

Section: Related Workmentioning

confidence: 99%

Verified Interactive Computation of Definite Integrals

Zhan

2021

Automated Deduction – CADE 28

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Symbolic computation is involved in many areas of mathematics, as well as in analysis of physical systems in science and engineering. Computer algebra systems present an easy-to-use interface for performing these calculations, but do not provide strong guarantees of correctness. In contrast, interactive theorem proving provides much stronger guarantees of correctness, but requires more time and expertise. In this paper, we propose a general framework for combining these two methods, and demonstrate it using computation of definite integrals. It allows the user to carry out step-by-step computations in a familiar user interface, while also verifying the computation by translating it to proofs in higher-order logic. The system consists of an intermediate language for recording computations, proof automation for simplification and inequality checking, and heuristic integration methods. A prototype is implemented in Python based on HolPy, and tested on a large collection of examples at the undergraduate level.

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“…c) Reachability analysis: At its most basic, reachability analysis is about identifying the set of states that a dynamical system could enter-the 'reachable states' or 'reachable set'given all admissible inputs and parameters [31]. A variety of methods exist for doing so; a common trade-off among these is that between approximation and computational inefficiency [32], [33].…”

Section: B Related Workmentioning

confidence: 99%

Cooperation for Scalable Supervision of Autonomy in Mixed Traffic

Hickert¹,

Li²,

Wu³

2021

Preprint

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Improvements in autonomy offer the potential for positive outcomes in a number of domains, yet guaranteeing their safe deployment is difficult. This work investigates how humans can intelligently supervise agents to achieve some level of safety even when performance guarantees are elusive. The motivating research question is: In safety-critical settings, can we avoid the need to have one human supervise one machine at all times? The paper formalizes this 'scaling supervision' problem, and investigates its application to the safety-critical context of autonomous vehicles (AVs) merging into traffic. It proposes a conservative, reachability-based method to reduce the burden on the AVs' human supervisors, which allows for the establishment of high-confidence upper bounds on the supervision requirements in this setting. Order statistics and traffic simulations with deep reinforcement learning show analytically and numerically that teaming of AVs enables supervision time sublinear in AV adoption. A key takeaway is that, despite present imperfections of AVs, supervision becomes more tractable as AVs are deployed en masse. While this work focuses on AVs, the scalable supervision framework is relevant to a broader array of autonomous control challenges.

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Set Propagation Techniques for Reachability Analysis

Cited by 140 publications

References 133 publications

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

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

Verified Interactive Computation of Definite Integrals

Cooperation for Scalable Supervision of Autonomy in Mixed Traffic

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