11,523 research outputs found
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
In this paper, we propose an approach to controller synthesis for a class of
constrained nonlinear systems. It is based on the use of a hybridization, that
is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined
on a triangulation of the state-space where on each simplex of the
triangulation, the nonlinear dynamics is conservatively approximated by an
affine system subject to disturbances. Except for the disturbances, this
hybridization can be seen as a piecewise affine hybrid system on simplices for
which appealing control synthesis techniques have been developed in the past
decade. We extend these techniques to handle systems subject to disturbances by
synthesizing and coordinating local robust affine controllers defined on the
simplices of the triangulation. We show that the resulting hybrid controller
can be used to control successfully the original constrained nonlinear system.
Our approach, though conservative, can be fully automated and is
computationally tractable. To show its effectiveness in practical applications,
we apply our method to control a pendulum mounted on a cart
Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights
In this paper, we present new results on consensus for continuous-time multi-
agent systems. We introduce the assumptions of persistent connectivity of the
interaction graph and of slow divergence of reciprocal interaction weights.
Persistent connectivity can be considered as the counterpart of the notion of
ultimate connectivity used in discrete- time consensus protocols. Slow
divergence of reciprocal interaction weights generalizes the assumption of
cut-balanced interactions. We show that under these two assumptions, the
continuous-time consensus protocol succeeds: the states of all the agents
converge asymptotically to a common value. Moreover, our proof allows us to
give an estimate of the rate of convergence towards the consensus. We also
provide two examples that make us think that both of our assumptions are tight
Nutrigenomics and immune function in fish : new insights from omics technologies
This study was funded by BBSRC grant BB/M026604/1.Peer reviewedPublisher PD
Time scale modeling for consensus in sparse directed networks with time-varying topologies
The paper considers the consensus problem in large networks represented by
time-varying directed graphs. A practical way of dealing with large-scale
networks is to reduce their dimension by collapsing the states of nodes
belonging to densely and intensively connected clusters into aggregate
variables. It will be shown that under suitable conditions, the states of the
agents in each cluster converge fast toward a local agreement. Local agreements
correspond to aggregate variables which slowly converge to consensus. Existing
results concerning the time-scale separation in large networks focus on fixed
and undirected graphs. The aim of this work is to extend these results to the
more general case of time-varying directed topologies. It is noteworthy that in
the fixed and undirected graph case the average of the states in each cluster
is time-invariant when neglecting the interactions between clusters. Therefore,
they are good candidates for the aggregate variables. This is no longer
possible here. Instead, we find suitable time-varying weights to compute the
aggregate variables as time-invariant weighted averages of the states in each
cluster. This allows to deal with the more challenging time-varying directed
graph case. We end up with a singularly perturbed system which is analyzed by
using the tools of two time-scales averaging which seem appropriate to this
system
Tweezers controlled resonator
We experimentally demonstrate trapping a microdroplet with an optical tweezer
and then enabling it as a microresonator by bringing it close to a tapered
fiber coupler. Our tweezers facilitated the tuning of the coupling from the
under-coupled to the critically coupled regime with an optical Q of 12 million
and microresonator size at the 85 mirons scale.Comment: 5 pages, 4 figure
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