Safety Verification of Nonlinear Hybrid Systems Based on Invariant Clusters

Kong, Hui; Bogomolov, Sergiy; Schilling, Christian; Jiang, Yu; Henzinger, Thomas A.

doi:10.1145/3049797.3049814

Cited by 20 publications

(35 citation statements)

References 30 publications

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“…Example 1 The following system, borrowed from [9], will be used as a running example. Consider N = 2, x = (x, y) and the vector field F = (y 2 , xy).…”

Section: Preliminariesmentioning

confidence: 99%

“…In particular, each subspace V i can be represented by a finite basis B i , which can be computed from the linear constraints on a in (8). From (9) it is then easy to check that ∪ i j=0 π ( j) [B i ] is a basis of J i . The termination conditions V m = V m+1 and J m = J m+1 can also be checked effectively.…”

Section: Computational Aspects Of Postmentioning

confidence: 99%

“…The system is given by the equations below, where the variables have the following meaning: u = axial velocity, w = vertical velocity, x = range, z = altitude, q = pitch rate, θ = pitch angle; we also have two equations encoding cos θ and sin θ. Applying the technique discussed in Remark 2, we also introduce the following auxiliary variables (parameters, hence 0 derivative): g = gravity acceleration, X/m, Z/m and M/I yy whose meaning is described in [23] (see also [8,9]); and u 0 , w 0 , x 0 , z 0 , q 0 , standing for the generic initial values of the corresponding variables. Overall, the system's vector field F 2 consists of 17 polynomials over as many variables.…”

Section: Airplanes Vertical Motionmentioning

confidence: 99%

See 2 more Smart Citations

Complete Algorithms for Algebraic Strongest Postconditions and Weakest Preconditions in Polynomial ODE’S

Boreale¹

2017

SOFSEM 2018: Theory and Practice of Computer Science

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A system of polynomial ordinary differential equations (ode's) is specified via a vector of multivariate polynomials, or vector field, F. A safety assertion ψ −→ [F] φ means that the system's trajectory will lie in a subset φ (the postcondition) of the state-space, whenever the initial state belongs to a subset ψ (the precondition). We consider the case when φ and ψ are algebraic varieties, that is, zero sets of polynomials. In particular, polynomials specifying the postcondition can be seen as conservation laws implied by ψ. Checking the validity of algebraic safety assertions is a fundamental problem in, for instance, hybrid systems. We consider generalized versions of this problem, and offer algorithms to: (1) given a user specified polynomial set P and a precondition ψ, find the smallest algebraic postcondition φ including the variety determined by the valid conservation laws in P (relativized strongest postcondition); (2) given a user specified postcondition φ, find the largest algebraic precondition ψ (weakest precondition). The first algorithm can also be used to find the weakest algebraic invariant of the system implying all conservation laws in P valid under ψ. The effectiveness of these algorithms is demonstrated on a few case studies from the literature.

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“…Example 1 The following system, borrowed from [9], will be used as a running example. Consider N = 2, x = (x, y) and the vector field F = (y 2 , xy).…”

Section: Preliminariesmentioning

confidence: 99%

Section: Computational Aspects Of Postmentioning

confidence: 99%

Section: Airplanes Vertical Motionmentioning

confidence: 99%

See 1 more Smart Citation

Complete Algorithms for Algebraic Strongest Postconditions and Weakest Preconditions in Polynomial ODE’S

Boreale¹

2017

SOFSEM 2018: Theory and Practice of Computer Science

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“…However, in the case of unsatisfiability these tools generally do not provide a reachable set representation that explains the verdict. Other techniques for reachability analysis of nonlinear systems include invariant generation [29,40,23,36,37], abstraction and hybridization [35,26,2,31,16,5].…”

Section: Introductionmentioning

confidence: 99%

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

Kong

Bartocci

Jiang

et al. 2019

Lecture Notes in Computer Science

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Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical systems without uncertainty. In this paper, we extend the approach with the ability to handle both continuous and hybrid dynamical systems with uncertainty that can reside in parameters and/or noise. We also improve the efficiency of the method significantly, by avoiding the use of interval-based methods for the enclosure-box computation without loosing soundness. We have developed a C++ prototype implementing the proposed approach and we evaluate it on several benchmarks. The experiments show that our approach is more efficient and precise than other methods in the literature. arXiv:1907.11514v1 [eess.SY]

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“…Reachability analysis of hybrid systems has been a major research issue over the past couple of decades [3,4,5,6,7,8]. An important part of the effort has been devoted to hybrid systems where the continuous dynamics is described by linear or affine differential equations or inclusions.…”

Section: Introductionmentioning

confidence: 99%

Conic Abstractions for Hybrid Systems

Bogomolov

Giacobbe

Henzinger

et al. 2017

Lecture Notes in Computer Science

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Abstract. Despite researchers' efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of boundedtime reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems.

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Safety Verification of Nonlinear Hybrid Systems Based on Invariant Clusters

Cited by 20 publications

References 30 publications

Complete Algorithms for Algebraic Strongest Postconditions and Weakest Preconditions in Polynomial ODE’S

Complete Algorithms for Algebraic Strongest Postconditions and Weakest Preconditions in Polynomial ODE’S

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

Conic Abstractions for Hybrid Systems

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