Reachability Analysis Using Polygonal Projections

Greenstreet, Mark R.; Mitchell, Ian M.

doi:10.1007/3-540-48983-5_12

Cited by 66 publications

(44 citation statements)

References 6 publications

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“…Computing reachable states for continuous or hybrid systems subject to bounded disturbances has become a major research issue in hybrid systems [ACH + 95], [G96], [CK98], [DM98], [CK03], [GM99], [ABDM00], [BT00], [MT00], [KV00], [D00] [ADG03], [G05], [F05]. One may argue that focusing on this question, which is concerned with transient behaviors of dynamical systems, can be seen as a major contribution of computer science to enriching the ensemble of standard questions (stability, controllability) traditionally posed in control [ABD + 00], [M02].…”

Section: Introductionmentioning

confidence: 99%

“…For hybrid systems in which the continuous dynamics has constant derivatives in every discrete state, such as timed automata or "linear" hybrid automata, the computation of the reachable states in a continuous phase is simply a matter of linear algebra [ACH + 95], [AMP95], [HHW97], [F05]. For systems with a non-trivial continuous dynamics, an approximation of the reachable states is generally computed by a combination of numerical integration and geometrical algorithms [GM99], [CK03], [ABDM00], [D00], [BT00], [KV00] [G05].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

Girard

Guernic²,

Maler

2006

Lecture Notes in Computer Science

226

213

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Abstract. This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

Girard

Guernic²,

Maler

2006

Lecture Notes in Computer Science

226

213

View full text Add to dashboard Cite

show abstract

“…The methods of the first category try to approximate reachable sets as accurately as possible by tracking their evolution under the continuous flows using some set represention (such as polyhedra, ellipsoids, level sets). This results in a variety of approximation schemes (such as [6,13,15,17,19,27,28,36,39,44,57]), and implemented by a number of tools such as Coho [28], CheckMate [15], d/dt [7], VeriShift [13], HYSDEL [58], MPT [45], HJB toolbox [44]. Since accurate reachable set approximations are computationally expensive, the methods of the second category seek approximations that are sufficiently good to prove the property of interest (such as barrier certificates [46], polynomial invariants [56]).…”

Section: Hybrid Systems Analysis: a Brief Reviewmentioning

confidence: 99%

“…As mentioned earlier, similar ideas have been used for numerical integration of nonlinear differential equations [22,26]. On the other hand, the reachability method proposed in [28] uses linear approximation in each integration step to obtain better approximations of the reachable sets in 2 dimensions. In [29], a control problem for a class of piecewise linear systems, similar to our affine hybridizations, is solved in terms of reachability conditions.…”

Section: From the Definition Of A(f) For All T ≥ T Z(t) ∈ A(f) Imentioning

confidence: 99%

Hybridization methods for the analysis of nonlinear systems

2007

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In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate.

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“…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]. Most of these approaches aim at providing an efficient way to obtain conservative but tight approximations to sets of reachable states for hybrid systems.…”

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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Reachability Analysis Using Polygonal Projections

Cited by 66 publications

References 6 publications

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

Hybridization methods for the analysis of nonlinear systems

Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement

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