8,642 research outputs found
Sapo: Reachability Computation and Parameter Synthesis of Polynomial Dynamical Systems
Sapo is a C++ tool for the formal analysis of polynomial dynamical systems.
Its main features are: 1) Reachability computation, i.e., the calculation of
the set of states reachable from a set of initial conditions, and 2) Parameter
synthesis, i.e., the refinement of a set of parameters so that the system
satisfies a given specification. Sapo can represent reachable sets as unions of
boxes, parallelotopes, or parallelotope bundles (symbolic representation of
polytopes). Sets of parameters are represented with polytopes while
specifications are formalized as Signal Temporal Logic (STL) formulas
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
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
Approximation of dynamical systems using S-systems theory : application to biological systems
In this paper we propose a new symbolic-numeric algorithm to find positive
equilibria of a n-dimensional dynamical system. This algorithm implies a
symbolic manipulation of ODE in order to give a local approximation of
differential equations with power-law dynamics (S-systems). A numerical
calculus is then needed to converge towards an equilibrium, giving at the same
time a S-system approximating the initial system around this equilibrium. This
algorithm is applied to a real biological example in 14 dimensions which is a
subsystem of a metabolic pathway in Arabidopsis Thaliana
Symbolic models for nonlinear control systems without stability assumptions
Finite-state models of control systems were proposed by several researchers
as a convenient mechanism to synthesize controllers enforcing complex
specifications. Most techniques for the construction of such symbolic models
have two main drawbacks: either they can only be applied to restrictive classes
of systems, or they require the exact computation of reachable sets. In this
paper, we propose a new abstraction technique that is applicable to any smooth
control system as long as we are only interested in its behavior in a compact
set. Moreover, the exact computation of reachable sets is not required. The
effectiveness of the proposed results is illustrated by synthesizing a
controller to steer a vehicle.Comment: 11 pages, 2 figures, journa
Lazy Abstraction-Based Controller Synthesis
We present lazy abstraction-based controller synthesis (ABCS) for
continuous-time nonlinear dynamical systems against reach-avoid and safety
specifications. State-of-the-art multi-layered ABCS pre-computes multiple
finite-state abstractions of varying granularity and applies reactive synthesis
to the coarsest abstraction whenever feasible, but adaptively considers finer
abstractions when necessary. Lazy ABCS improves this technique by constructing
abstractions on demand. Our insight is that the abstract transition relation
only needs to be locally computed for a small set of frontier states at the
precision currently required by the synthesis algorithm. We show that lazy ABCS
can significantly outperform previous multi-layered ABCS algorithms: on
standard benchmarks, lazy ABCS is more than 4 times faster
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