Model Checking of Hybrid Systems: From Reachability Towards Stability

Podelski, Andreas; Wagner, Silke

doi:10.1007/11730637_38

Cited by 58 publications

(44 citation statements)

References 22 publications

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“…Region stability is similar to our notion of persistence [45], which requires all trajectories to eventually reach some region of the state space. Sound and complete proof rules for establishing region stability have been explored and automated [47], as have more efficient encodings of the proof rule that scale better in dimensionality [31].…”

Section: Related Workmentioning

confidence: 92%

“…Sound and complete proof rules for establishing region stability have been explored and automated [47], as have more efficient encodings of the proof rule that scale better in dimensionality [31]. However, all algorithms we are aware of for checking region stability require linear or simpler (timed or rectangular) ODEs [45,47,46,31,11,48]. Strong attractors are basins of attraction where every state in the state space eventually reaches a region of the state space [45].…”

Section: Related Workmentioning

confidence: 99%

“…However, all algorithms we are aware of for checking region stability require linear or simpler (timed or rectangular) ODEs [45,47,46,31,11,48]. Strong attractors are basins of attraction where every state in the state space eventually reaches a region of the state space [45]. Some algorithms do not check region stability, but actually check stronger properties such as strong attraction, that imply region stability [45].…”

Section: Related Workmentioning

confidence: 99%

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Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Sogokon

Jackson

Johnson

2017

Lecture Notes in Computer Science

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We propose a method for verifying persistence of nonlinear hybrid systems. Given some system and an initial set of states, the method can guarantee that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flow-pipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study concerning showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flow-pipes or just reasoning about invariants alone can be insufficient. The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property with the aid of an automatic prover specifically designed for handling transcendental functions.

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Section: Related Workmentioning

confidence: 92%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Sogokon

Jackson

Johnson

2017

Lecture Notes in Computer Science

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“…In order to quantitatively define the motion capabilities of the robots, we consider the following temporal operators 3, 2, 32 and the universal path quantifier A as defined in [25,26]. Consider an initial set F s and a set F with F s , F ⊆ Y .…”

Section: Robot Modelmentioning

confidence: 99%

A framework for multi-robot motion planning from temporal logic specifications

Koo

Quottrup

et al. 2012

Sci. China Inf. Sci.

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We propose a framework for the coordination of a network of robots with respect to formal requirement specifications expressed in temporal logics. A regular tessellation is used to partition the space of interest into a union of disjoint regular and equal cells with finite facets, and each cell can only be occupied by a robot or an obstacle. Each robot is assumed to be equipped with a finite collection of continuous-time nonlinear closed-loop dynamics to be operated in. The robot is then modeled as a hybrid automaton for capturing the finitely many modes of operation for either staying within the current cell or reaching an adjacent cell through the corresponding facet. By taking the motion capabilities into account, a bisimilar discrete abstraction of the hybrid automaton can be constructed. Having the two systems bisimilar, all properties that are expressible in temporal logics such as Linear-time Temporal Logic, Computation Tree Logic, and µ-calculus can be preserved. Motion planning can then be performed at a discrete level by considering the parallel composition of discrete abstractions of the robots with a requirement specification given in a suitable temporal logic. The bisimilarity ensures that the discrete planning solutions are executable by the robots. For demonstration purpose, a finite automaton is used as the abstraction and the requirement specification is expressed in Computation Tree Logic. The model checker Cadence SMV is used to generate coordinated verified motion planning solutions. Two autonomous aerial robots are used to demonstrate how the proposed framework may be applied to solve coordinated motion planning problems.

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“…Specifically, it has been proposed for verifying liveness properties in the form of ranking functions, transition invariants and progress invariants [23,22,6,24,10]. However, there are some important distinctions.…”

Section: Related Workmentioning

confidence: 99%

Switching logic synthesis for reachability

Taly

Tiwari

2010

Proceedings of the Tenth ACM International Conference on Embedded Software

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We consider the problem of driving a system from some initial configuration to a desired configuration while avoiding some unsafe configurations. The system to be controlled is a dynamical system that can operate in different modes. The goal is to synthesize the logic for switching between the modes so that the desired reachability property holds.In this paper, we first present a sound and complete inference rule for proving reachability properties of single mode continuous dynamical systems. Next, we present an inference rule for proving controlled reachability in multi-modal continuous dynamical systems. From a constructive proof of controlled reachability, we show how to synthesize the desired switching logic. We show that our synthesis procedure is sound and produces only non-zeno hybrid systems.In practice, we perform a constructive proof of controlled reachability by solving an Exists-Forall formula in the theory of reals. We present an approach for solving such formulas that combines symbolic and numeric solvers. We demonstrate our approach on some examples. All results extend naturally to the case when, instead of reachability, interest is in until properties.

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Model Checking of Hybrid Systems: From Reachability Towards Stability

Cited by 58 publications

References 22 publications

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

A framework for multi-robot motion planning from temporal logic specifications

Switching logic synthesis for reachability

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