21,953 research outputs found
The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations
This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(āĪµ) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(Īµ) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter Īµ is not precisely known. Ā© 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh
The Accelerating Universe
In this article we review the discovery of the accelerating universe using
type Ia supernovae. We then outline ways in which dark energy - component that
causes the acceleration - is phenomenologically described. We finally describe
principal cosmological techniques to measure large-scale properties of dark
energy. This chapter complements other articles in this book that describe
theoretical understanding (or lack thereof) of the cause for the accelerating
universe.Comment: Invited review chapter for book "Adventures in Cosmology" (ed. D.
Goodstein) aimed at general scientists; 28 pages, 10 figure
The necessary and sufficient condition for an algebraic integer to be a Salem number
We present a necessary and sufficient condition for a root greater than unity
of a monic reciprocal polynomial of an even degree at least four, with integer
coefficients, to be a Salem number. We determine the probability of fulfillment
the condition for an arbitrary power of the root.Comment: 13 pages, 2 figures, 2 table
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