A New Class of Decidable Hybrid Systems

Lafferriere, Gerardo; Pappas, George J.; Yovine, Sergio

doi:10.1007/3-540-48983-5_15

Cited by 155 publications

(127 citation statements)

References 17 publications

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“…Lafferriere et al [12] gave important decidability results for hybrid systems with some classes of linear continuous dynamics but only random discrete resets. These results do not apply to air traffic maneuvers, because these maneuvers have non-trivial resets: the aircraft's position does not just jump randomly when switching modes but, rather, systematically according to the maneuver.…”

Section: Related Workmentioning

confidence: 99%

“…12, because the resulting formulas of the form ∀t≥0 G(x 1 (t), x 2 (t), ϑ(t)) involve quantified arithmetic over trigonometric functions, which is undecidable. The flight equations F(ω) and G( ) given in Section 4.1 can be derived from equation (12). These equations F(ω) and G( ) still have just as complicated trigonometric solutions, but the differential equations themselves are polynomials in the state variables, which is crucial for differential invariants [17,22].…”

Section: A1 Transcendental Functions Make Flight Dynamics Difficultmentioning

confidence: 99%

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Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Platzer

Clarke

2009

FM 2009: Formal Methods

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Aircraft collision avoidance maneuvers are important and complex applications. Curved flight exhibits nontrivial continuous behavior. In combination with the control choices during air traffic maneuvers, this yields hybrid systems with challenging interactions of discrete and continuous dynamics. As a case study illustrating the use of a new proof assistant for a logic for nonlinear hybrid systems, we analyze collision freedom of roundabout maneuvers in air traffic control, where appropriate curved flight, good timing, and compatible maneuvering are crucial for guaranteeing safe spatial separation of aircraft throughout their flight. We show that formal verification of hybrid systems can scale to curved flight maneuvers required in aircraft control applications. We introduce a fully flyable variant of the roundabout collision avoidance maneuver and verify safety properties by compositional verification.

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Section: Related Workmentioning

confidence: 99%

Section: A1 Transcendental Functions Make Flight Dynamics Difficultmentioning

confidence: 99%

Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Platzer

Clarke

2009

FM 2009: Formal Methods

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“…If H is an o-minimal automata, then T H admits finite bisimulation [13,14,7]. This result does not guarantee the decidability of the entire family [14], because the bisimulation reduction is not computable, in general, for o-minimal automata. In order to decide reachability relying on bisimulation reduction, it is necessary to effectively:…”

Section: Related Workmentioning

confidence: 97%

“…In this paper we consider a class of hybrid automata called o-minimal automata [13,14]. O-minimal theories, introduced below, play a central role in the definition of o-minimal automata.…”

Section: O-minimal Theories and O-minimal Hybrid Automatamentioning

confidence: 99%

Reachability Problems on Extended O-Minimal Hybrid Automata

Gentilini

2005

Lecture Notes in Computer Science

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Abstract. Within hybrid systems theory, o-minimal automata are often considered on the border between decidability and undecidability. In such classes of hybrid automata, the constraint of having only constant reset upon discrete jumps is a strong limitation for their applicability: hence, an important issue for both theoreticians and practitioners, is that of relaxing the above constraint, while not fall into undecidability.In this paper we start considering the problem of timed-bounded reachability on o-minimal automata. This can be seen either as a reachability problem paired with time-constraints or as a classical reachability problem for a class of hybrid automata which properly extends the o-minimal one, with an extra variable representing time. Then, we directly face the problem of extending o-minimal automata by allowing some variables to retain their values upon a discrete jump, without crossing the undecidability border.

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“…The computation of sets of successors states is usually the most expensive step in hybrid system verification. Moreover, successor sets can be computed and represented exactly only for certain sub-classes of hybrid systems [15,16]. However, several approaches to over-approximate successor sets have been published, as e. g., successor set approximations by orthogonal polyhedra [17], general polyhedra [18], projections to lower dimensional polyhedra [19], or ellipsoids [20].…”

Section: Refinement Of Abstractions For Hybrid Systemsmentioning

confidence: 99%

Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement

Clarke

Fehnker

Han

et al. 2003

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finite-state abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of infinite-state systems, in particular of hybrid systems. Following an approach originally developed for finite-state systems [1, 2], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. A detailed example illustrates our counterexample-guided refinement procedure. Experimental results for a prototype implementation of the procedure indicate its advantages over existing methods.

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A New Class of Decidable Hybrid Systems

Cited by 155 publications

References 17 publications

Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Reachability Problems on Extended O-Minimal Hybrid Automata

Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement

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