A Small Model Theorem for Rectangular Hybrid Automata Networks

Johnson, Taylor T.; Mitra, Sayan

doi:10.1007/978-3-642-30793-5_2

Cited by 25 publications

(19 citation statements)

References 40 publications

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“…We evaluated HAHA on variations of our running problem and on examples from the Passel benchmark suite [Johnson and Mitra, 2012b]. In the following sections, we describe the results of the verification of some of the safety conditions presented throughout the paper.…”

Section: Methodsmentioning

confidence: 99%

“…[Henzinger et al, 2001] analyzes the interplay of fixed combinations of hybrid systems using assume-guarantee reasoning. In Mitra, 2012a, Johnson andMitra, 2012b] a small model theorem for finite families of automata with constant derivatives, with a parametric bound on the number of components, is established; the discrete transitions describe changes in exactly one system (thus no global updates of sensors can be modeled). Our approach allows us to consider families with an unbounded or infinite number of components which are parametric linear hybrid automata.…”

Section: Related Workmentioning

confidence: 99%

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Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata

Damm

Horbach

Sofronie-Stokkermans

2015

Frontiers of Combining Systems

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We consider systems composed of an unbounded number of uniformly designed linear hybrid automata, whose dynamic behavior is determined by their relation to neighboring systems. We present a class of such systems and a class of safety properties whose verification can be reduced to the verification of (small) families of "neighboring" systems of bounded size, and identify situations in which such verification problems are decidable, resp. fixed parameter tractable. We illustrate the approach with an example from coordinated vehicle guidance, and describe an implementation which allows us to perform such verification tasks automatically.

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Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata

Damm

Horbach

Sofronie-Stokkermans

2015

Frontiers of Combining Systems

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“…For instance, several drones of the type described in Example 1 share the same dynamics but they may have different initial conditions and follow different waypoints. This commonality has been exploited in developing specialized proof techniques [22]. For reachability analysis, using symmetry transforms of the previous section, reachtubes of one agent in one mode can be used to get the reachtubes of other modes and even other agents.…”

Section: Virtual Systemmentioning

confidence: 99%

Multi-agent Safety Verification Using Symmetry Transformations

Sibai

Mokhlesi

Fan

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

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We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map solutions and to other solutions. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of virtual system which define symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of virtual system, we present a prototype tool CacheReach that builds a cache of reachtubes for this system, in a way that is agnostic of the representation of the reachsets and the reachability analysis subroutine used.Our experimental evaluation of CacheReach shows up to 66% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.

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“…Additionally, only neighboring cells communicate with one another and the communication topology is fixed (aside from failures). For these reasons, this problem can serve as a case study in automatic parameterized verification of distributed cyber-physical systems [28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Safe and stabilizing distributed multi-path cellular flows

Johnson

Mitra

2015

Theoretical Computer Science

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We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (robots, vehicles, etc.) within each partition (cell) is coupled. Establishing liveness in such systems is challenging, but such analysis will be necessary to apply such distributed traffic control algorithms in applications like coordinating robot swarms and the intelligent highway system. We present a formal model of a distributed traffic control protocol that guarantees minimum separation between entities, even as some cells fail. Once new failures cease occurring, in the case of a single target, the protocol is guaranteed to self-stabilize and the entities with feasible paths to the target cell make progress towards it. For multiple targets, failures may cause deadlocks in the system, so we identify a class of non-deadlocking failures where all entities are able to make progress to their respective targets. The algorithm relies on two general principles: temporary blocking for maintenance of safety and local geographical routing for guaranteeing progress. Our assertional proofs may serve as a template for the analysis of other distributed traffic control protocols. We present simulation results that provide estimates of throughput as a function of entity velocity, safety separation, single-target path complexity, failure-recovery rates, and multi-target path complexity.

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A Small Model Theorem for Rectangular Hybrid Automata Networks

Cited by 25 publications

References 40 publications

Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata

Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata

Multi-agent Safety Verification Using Symmetry Transformations

Safe and stabilizing distributed multi-path cellular flows

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