80 research outputs found
Quadratic-exponential coherent feedback control of linear quantum stochastic systems
This paper considers a risk-sensitive optimal control problem for a
field-mediated interconnection of a quantum plant with a coherent
(measurement-free) quantum controller. The plant and the controller are
multimode open quantum harmonic oscillators governed by linear quantum
stochastic differential equations, which are coupled to each other and driven
by multichannel quantum Wiener processes modelling the external bosonic fields.
The control objective is to internally stabilize the closed-loop system and
minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential
functional which penalizes the plant variables and the controller output. We
obtain first-order necessary conditions of optimality for this problem by
computing the partial Frechet derivatives of the cost functional with respect
to the energy and coupling matrices of the controller in frequency domain and
state space. An infinitesimal equivalence between the risk-sensitive and
weighted coherent quantum LQG control problems is also established. In addition
to variational methods, we employ spectral factorizations and infinite cascades
of auxiliary classical systems. Their truncations are applicable to numerical
optimization algorithms (such as the gradient descent) for coherent quantum
risk-sensitive feedback synthesis.Comment: 29 pages, 3 figure
Towards effective information content assessment: analytical derivation of information loss in the reconstruction of random fields with model uncertainty
Structures are abundant in both natural and human-made environments and
usually studied in the form of images or scattering patterns. To characterize
structures a huge variety of descriptors is available spanning from porosity to
radial and correlation functions. In addition to morphological structural
analysis, such descriptors are necessary for stochastic reconstructions,
stationarity and representativity analysis. The most important characteristic
of any such descriptor is its information content - or its ability to describe
the structure at hand. For example, from crystallography it is well known that
experimentally measurable correlation function lacks necessary
information content to describe majority of structures. The information content
of this function can be assessed using Monte-Carlo methods only for very small
2D images due to computational expenses. Some indirect quantitative approaches
for this and other correlation function were also proposed. Yet, to date no
methodology to obtain information content for arbitrary 2D or 3D image is
available. In this work, we make a step toward developing a general framework
to perform such computations analytically. We show, that one can assess the
entropy of a perturbed random field and that stochastic perturbation of fields
correlation function decreases its information content. In addition to
analytical expression, we demonstrate that different regions of correlation
function are in different extent informative and sensitive for perturbation.
Proposed model bridges the gap between descriptor-based heterogeneous media
reconstruction and information theory and opens way for computationally
effective way to compute information content of any descriptor as applied to
arbitrary structure.Comment: Keywords: correlation functions, structure characterization,
structural descriptors, image analysis, information conten
Efficient optical communication in a turbulent atmosphere.
Also issued as a Ph.D. thesis in the Dept. of Electrical Engineering, 1969.Bibliography: p.113-117
Efficient optical communication in a turbulent atmosphere
Efficient optical communication in atmospheric turbulenc
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