58,506 research outputs found

### On Weak Topology for Optimal Control of Switched Nonlinear Systems

Optimal control of switched systems is challenging due to the discrete nature
of the switching control input. The embedding-based approach addresses this
challenge by solving a corresponding relaxed optimal control problem with only
continuous inputs, and then projecting the relaxed solution back to obtain the
optimal switching solution of the original problem. This paper presents a novel
idea that views the embedding-based approach as a change of topology over the
optimization space, resulting in a general procedure to construct a switched
optimal control algorithm with guaranteed convergence to a local optimizer. Our
result provides a unified topology based framework for the analysis and design
of various embedding-based algorithms in solving the switched optimal control
problem and includes many existing methods as special cases

### Partial Information Differential Games for Mean-Field SDEs

This paper is concerned with non-zero sum differential games of mean-field
stochastic differential equations with partial information and convex control
domain. First, applying the classical convex variations, we obtain stochastic
maximum principle for Nash equilibrium points. Subsequently, under additional
assumptions, verification theorem for Nash equilibrium points is also derived.
Finally, as an application, a linear quadratic example is discussed. The unique
Nash equilibrium point is represented in a feedback form of not only the
optimal filtering but also expected value of the system state, throughout the
solutions of the Riccati equations.Comment: 7 page

### Focused information criterion and model averaging for generalized additive partial linear models

We study model selection and model averaging in generalized additive partial
linear models (GAPLMs). Polynomial spline is used to approximate nonparametric
functions. The corresponding estimators of the linear parameters are shown to
be asymptotically normal. We then develop a focused information criterion (FIC)
and a frequentist model average (FMA) estimator on the basis of the
quasi-likelihood principle and examine theoretical properties of the FIC and
FMA. The major advantages of the proposed procedures over the existing ones are
their computational expediency and theoretical reliability. Simulation
experiments have provided evidence of the superiority of the proposed
procedures. The approach is further applied to a real-world data example.Comment: Published in at http://dx.doi.org/10.1214/10-AOS832 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### A variant of Horn's problem and derivative principle

Identifying the spectrum of the sum of two given Hermitian matrices with
fixed eigenvalues is the famous Horn's problem.In this note, we investigate a
variant of Horn's problem, i.e., we identify the probability density function
(abbr. pdf) of the diagonals of the sum of two random Hermitian matrices with
given spectra. We then use it to re-derive the pdf of the eigenvalues of the
sum of two random Hermitian matrices with given eigenvalues via
\emph{derivative principle}, a powerful tool used to get the exact probability
distribution by reducing to the corresponding distribution of diagonal
entries.We can recover Jean-Bernard Zuber's recent results on the pdf of the
eigenvalues of two random Hermitian matrices with given eigenvalues. Moreover,
as an illustration, we derive the analytical expressions of eigenvalues of the
sum of two random Hermitian matrices from \rG\rU\rE(n) or Wishart ensemble by
derivative principle, respectively.We also investigate the statistics of
exponential of random matrices and connect them with Golden-Thompson
inequality, and partly answer a question proposed by Forrester. Some potential
applications in quantum information theory, such as uniform average quantum
Jensen-Shannon divergence and average coherence of uniform mixture of two
orbits,are discussed.Comment: 24 pages, LaTeX; a new result, i.e., Theorem 3.7, is added and
several references are include

### Research of the active reflector antenna using laser angle metrology system

Active reflector is one of the key technologies for constructing large
telescopes, especially for the millimeter/sub-millimeter radio telescopes. This
article introduces a new efficient laser angle metrology system for the active
reflector antenna of the large radio telescopes, with a plenty of active
reflector experiments mainly about the detecting precisions and the maintaining
of the surface shape in real time, on the 65-meter radio telescope prototype
constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT).
The test results indicate that the accuracy of the surface shape segmenting and
maintaining is up to micron dimension, and the time-response can be of the
order of minutes. Therefore, it is proved to be workable for the sub-millimeter
radio telescopes.Comment: 10 pages, 15 figure

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