33,663 research outputs found
Safety verification of nonlinear hybrid systems based on invariant clusters
In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient
Coordinated Robot Navigation via Hierarchical Clustering
We introduce the use of hierarchical clustering for relaxed, deterministic
coordination and control of multiple robots. Traditionally an unsupervised
learning method, hierarchical clustering offers a formalism for identifying and
representing spatially cohesive and segregated robot groups at different
resolutions by relating the continuous space of configurations to the
combinatorial space of trees. We formalize and exploit this relation,
developing computationally effective reactive algorithms for navigating through
the combinatorial space in concert with geometric realizations for a particular
choice of hierarchical clustering method. These constructions yield
computationally effective vector field planners for both hierarchically
invariant as well as transitional navigation in the configuration space. We
apply these methods to the centralized coordination and control of
perfectly sensed and actuated Euclidean spheres in a -dimensional ambient
space (for arbitrary and ). Given a desired configuration supporting a
desired hierarchy, we construct a hybrid controller which is quadratic in
and algebraic in and prove that its execution brings all but a measure zero
set of initial configurations to the desired goal with the guarantee of no
collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in
preparation for submission to a journa
Cluster synchronization in networks of coupled non-identical dynamical systems
In this paper, we study cluster synchronization in networks of coupled
non-identical dynamical systems. The vertices in the same cluster have the same
dynamics of uncoupled node system but the uncoupled node systems in different
clusters are different. We present conditions guaranteeing cluster
synchronization and investigate the relation between cluster synchronization
and the unweighted graph topology. We indicate that two condition play key
roles for cluster synchronization: the common inter-cluster coupling condition
and the intra-cluster communication. From the latter one, we interpret the two
well-known cluster synchronization schemes: self-organization and driving, by
whether the edges of communication paths lie at inter or intra-cluster. By this
way, we classify clusters according to whether the set of edges inter- or
intra-cluster edges are removable if wanting to keep the communication between
pairs of vertices in the same cluster. Also, we propose adaptive feedback
algorithms on the weights of the underlying graph, which can synchronize any
bi-directed networks satisfying the two conditions above. We also give several
numerical examples to illustrate the theoretical results
Persistent Transport Barrier on the West Florida Shelf
Analysis of drifter trajectories in the Gulf of Mexico has revealed the
existence of a region on the southern portion of the West Florida Shelf (WFS)
that is not visited by drifters that are released outside of the region. This
so-called ``forbidden zone'' (FZ) suggests the existence of a persistent
cross-shelf transport barrier on the southern portion of the WFS. In this
letter a year-long record of surface currents produced by a Hybrid-Coordinate
Ocean Model simulation of the WFS is used to identify Lagrangian coherent
structures (LCSs), which reveal the presence of a robust and persistent
cross-shelf transport barrier in approximately the same location as the
boundary of the FZ. The location of the cross-shelf transport barrier undergoes
a seasonal oscillation, being closer to the coast in the summer than in the
winter. A month-long record of surface currents inferred from high-frequency
(HF) radar measurements in a roughly 60 km 80 km region on the WFS off
Tampa Bay is also used to identify LCSs, which reveal the presence of robust
transient transport barriers. While the HF-radar-derived transport barriers
cannot be unambiguously linked to the boundary of the FZ, this analysis does
demonstrate the feasibility of monitoring transport barriers on the WFS using a
HF-radar-based measurement system. The implications of a persistent cross-shelf
transport barrier on the WFS for the development of harmful algal blooms on the
shoreward side of the barrier are considered.Comment: Submitted to Geophysical Research Letter
Hypernuclei, dibaryon and antinuclei production in high energy heavy ion collisions: Thermal production vs. Coalescence
We study the production of (hyper-)nuclei and di-baryons in most central
heavy Ion collisions at energies of GeV. In particular we are
interested in clusters produced from the hot and dense fireball. The formation
rate of strange and non-strange clusters is estimated by assuming thermal
production from the intermediate phase of the UrQMD-hydro hybrid model and
alternatively by the coalescence mechanism from a hadronic cascade model. Both
model types are compared in detail. For most energies we find that both
approaches agree in their predictions for the yields of the clusters. Only for
very low beam energies, and for di-baryons including 's, we observe
considerable differences. We also study the production of anti-matter clusters
up to top RHIC energies and show that the observation of anti- and even
anti- is feasible. We have found a considerable qualitative
difference in the energy dependence of the strangeness population factor
when comparing the thermal production with the coalescence results.Comment: 9 pages, 8 figures and 2 tables, version accepted by PL
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