116,367 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
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
Equal Entries in Totally Positive Matrices
We show that the maximal number of equal entries in a totally positive (resp.
totally nonsingular) matrix is (resp.
)). Relationships with point-line incidences in the plane,
Bruhat order of permutations, and completability are also presented. We
also examine the number and positionings of equal minors in a
matrix, and give a relationship between the location of
equal minors and outerplanar graphs.Comment: 15 page
Robust Component-based Network Localization with Noisy Range Measurements
Accurate and robust localization is crucial for wireless ad-hoc and sensor
networks. Among the localization techniques, component-based methods advance
themselves for conquering network sparseness and anchor sparseness. But
component-based methods are sensitive to ranging noises, which may cause a huge
accumulated error either in component realization or merging process. This
paper presents three results for robust component-based localization under
ranging noises. (1) For a rigid graph component, a novel method is proposed to
evaluate the graph's possible number of flip ambiguities under noises. In
particular, graph's \emph{MInimal sepaRators that are neaRly cOllineaR
(MIRROR)} is presented as the cause of flip ambiguity, and the number of
MIRRORs indicates the possible number of flip ambiguities under noise. (2) Then
the sensitivity of a graph's local deforming regarding ranging noises is
investigated by perturbation analysis. A novel Ranging Sensitivity Matrix (RSM)
is proposed to estimate the node location perturbations due to ranging noises.
(3) By evaluating component robustness via the flipping and the local deforming
risks, a Robust Component Generation and Realization (RCGR) algorithm is
developed, which generates components based on the robustness metrics. RCGR was
evaluated by simulations, which showed much better noise resistance and
locating accuracy improvements than state-of-the-art of component-based
localization algorithms.Comment: 9 pages, 15 figures, ICCCN 2018, Hangzhou, Chin
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