136,615 research outputs found
Local Nash Realizations
In this paper we investigate realization theory of a class of non-linear
systems, called Nash systems. Nash systems are non-linear systems whose vector
fields and readout maps are analytic semi-algebraic functions. In this paper we
will present a characterization of minimality in terms of observability and
reachability and show that minimal Nash systems are isomorphic. The results are
local in nature, i.e. they hold only for small time intervals. The hope is that
the presented results can be extended to hold globally.Comment: 8 pages, extended conference pape
Scaling limits for the critical Fortuin-Kastelyn model on a random planar map II: local estimates and empty reduced word exponent
We continue our study of the inventory accumulation introduced by Sheffield
(2011), which encodes a random planar map decorated by a collection of loops
sampled from the critical Fortuin-Kasteleyn (FK) model. We prove various
\emph{local estimates} for the inventory accumulation model, i.e., estimates
for the precise number of symbols of a given type in a reduced word sampled
from the model. Using our estimates, we obtain the scaling limit of the
associated two-dimensional random walk conditioned on the event that it stays
in the first quadrant for one unit of time and ends up at a particular position
in the interior of the first quadrant. We also obtain the exponent for the
probability that a word of length sampled from the inventory accumulation
model corresponds to an empty reduced word, which is equivalent to an
asymptotic formula for the partition function of the critical FK planar map
model. The estimates of this paper will be used in a subsequent paper to obtain
the scaling limit of the lattice walk associated with a finite-volume FK planar
map.Comment: 49 pages, 2 figures; final version published in EJP. Changes include
significantly approved exposition and relation to partition functio
Feedback in Tournaments under Commitment Problems: The-ory and Experimental Evidence
In this paper, we analyze a principal's optimal feedback policy in tournaments. We close a gap in the literature by assuming the principal to be unable to commit to a certain policy at the beginning of the tournament. Our analysis shows that in equilibrium the principal reveals in-termediate information regarding the agents’ previous performances if these performances are not too different. Moreover, we investigate a situation where the principal is not able to credi-bly communicate her information. Having presented our formal analysis, we test these results using data from laboratory experiments. The experimental findings provide some support for the model
Finite-time behavior of inner systems
In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller
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