26 research outputs found
Hybrid Automata in Systems Biology: How far can we go?
We consider the reachability problem on semi-algebraic hybrid automata. In particular, we deal with the effective cost that has to be afforded to solve reachability through first-order satisfiability.
The analysis we perform with some existing tools shows that even simple examples cannot be efficiently solved. We need approximations to reduce the number of variables in our formulae: this is the main source of time computation growth. We study standard approximation methods based on Taylor polynomials and ad-hoc strategies to solve the problem and we show their effectiveness on the repressilator case study
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Approximating the set of reachable states of a dynamical system is an
algorithmic yet mathematically rigorous way to reason about its safety.
Although progress has been made in the development of efficient algorithms for
affine dynamical systems, available algorithms still lack scalability to ensure
their wide adoption in the industrial setting. While modern linear algebra
packages are efficient for matrices with tens of thousands of dimensions,
set-based image computations are limited to a few hundred. We propose to
decompose reach set computations such that set operations are performed in low
dimensions, while matrix operations like exponentiation are carried out in the
full dimension. Our method is applicable both in dense- and discrete-time
settings. For a set of standard benchmarks, it shows a speed-up of up to two
orders of magnitude compared to the respective state-of-the art tools, with
only modest losses in accuracy. For the dense-time case, we show an experiment
with more than 10.000 variables, roughly two orders of magnitude higher than
possible with previous approaches
LNCS
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 bounded-time 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
Adaptive Parameter Tuning for Reachability Analysis of Linear Systems
Despite the possibility to quickly compute reachable sets of large-scale
linear systems, current methods are not yet widely applied by practitioners.
The main reason for this is probably that current approaches are not
push-button-capable and still require to manually set crucial parameters, such
as time step sizes and the accuracy of the used set representation---these
settings require expert knowledge. We present a generic framework to
automatically find near-optimal parameters for reachability analysis of linear
systems given a user-defined accuracy. To limit the computational overhead as
much as possible, our methods tune all relevant parameters during runtime. We
evaluate our approach on benchmarks from the ARCH competition as well as on
random examples. Our results show that our new framework verifies the selected
benchmarks faster than manually-tuned parameters and is an order of magnitude
faster compared to genetic algorithms
Reachability of Uncertain Linear Systems Using Zonotopes
International audienceWe present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties : they can be encoded efficiently, they are closed under linear transformations and Minkowski sum. The resulting method has been used to treat several examples and has shown great performances for high dimensional systems. An extension of the method for the verification of piecewise linear hybrid systems is proposed