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(√ε) 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(ε) 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 ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

Fast approximation of centrality and distances in hyperbolic graphs

We show that the eccentricities (and thus the centrality indices) of all vertices of a $\delta$-hyperbolic graph $G=(V,E)$ can be computed in linear time with an additive one-sided error of at most $c\delta$, i.e., after a linear time preprocessing, for every vertex $v$ of $G$ one can compute in $O(1)$ time an estimate $\hat{e}(v)$ of its eccentricity $ecc_G(v)$ such that $ecc_G(v)\leq \hat{e}(v)\leq ecc_G(v)+ c\delta$ for a small constant $c$. We prove that every $\delta$-hyperbolic graph $G$ has a shortest path tree, constructible in linear time, such that for every vertex $v$ of $G$, $ecc_G(v)\leq ecc_T(v)\leq ecc_G(v)+ c\delta$. These results are based on an interesting monotonicity property of the eccentricity function of hyperbolic graphs: the closer a vertex is to the center of $G$, the smaller its eccentricity is. We also show that the distance matrix of $G$ with an additive one-sided error of at most $c'\delta$ can be computed in $O(|V|^2\log^2|V|)$ time, where $c'< c$ is a small constant. Recent empirical studies show that many real-world graphs (including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others) have small hyperbolicity. So, we analyze the performance of our algorithms for approximating centrality and distance matrix on a number of real-world networks. Our experimental results show that the obtained estimates are even better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author

Selecting frequency and parameters of DC-fault tolerant Non-Isolated high power MMC DC/DC Converter

Peer reviewedPostprin

Advances in water mains network modelling for improved operations

Published© 2015 The Authors. Published by Elsevier Ltd. The traditional approach to water mains network model calibration is too coarse. System and data anomalies impact on the simulated pressures in the models. These include unknown status valves, incorrect pipe data including pipe roughness values and unknown leaks. A combination of smarter field testing and staged optimisation analyses provides a promising solution to solving this complex problem. An anonymous model has been used to demonstrate that inclusion in the field test of planned hydrant discharges and concurrent tactical valve operations will help detect the unknown status valves but also lead to more accurate pipe roughness values and leakage hotspots

Testing two isolates of diaporthe/phomopsis helianthi in a population of sunflower recombinant inbred lines

Development of new, more aggressive isolates of Phomopsis helianthi in Serbia and Montenegro has been investigated. Two isolates of Phomopsis helianthi Yu 4 and Yu 12, had been found on the stem of NS-H-45, a highly tolerant sunflower hybrid. The isolate Yu 4 was isolated in the northern part of the Vojvodina Province, a region where Phomopsis typically occurs. The isolate Yu 12 comes from the southern part of the Vojvodina Province, a region along the Danube River, which suffered an intensive outbreak of Phomopsis in 1997. A preliminary study of the isolates showed that these two isolates were significantly different for radial growth in Petri dish. A test was thus made with recombinant inbred lines in the F9 generation developed from the cross of LR-4-17 (inbred line with high tolerance to Phomopsis) and HA-89 (susceptible inbred line). Experiments were conducted in the greenhouse inoculating plant leaf tips with the mycelium of the fungus. The test showed that there were no significant differences between the two isolates, Yu 4 and Yu 12. It was concluded that the intensive attack recorded in 1997 along the Danube River occurred due to exceptionally favorable environmental conditions for the development of the disease

Localization of the relative phase via measurements

When two independently-prepared Bose-Einstein condensates are released from their corresponding traps, the absorbtion image of the overlapping clouds presents an interference pattern. Here we analyze a model introduced by Javanainen and Yoo (J. Javanainen and S. M. Yoo, Phys. Rev. Lett. 76, 161 (1996)), who considered two atomic condensates described by plane waves propagating in opposite directions. We present an analytical argument for the measurement-induced breaking of the relative phase symmetry in this system, demonstrating how the phase gets localized after a large enough number of detection events.Comment: 8 pages, 1 figur

Magnetotunnelling in resonant tunnelling structures with spin-orbit interaction

Magnetotunnelling spectroscopy of resonant tunnelling structures provides information on the nature of the two-dimensional electron gas in the well. We describe a model based on nonequilibrium Green's functions that allows for a comprehensive study of the density of states, tunnelling currents and current spin polarization. The investigated effects include the electron-phonon interaction, interface roughness scattering, Zeeman effect and the Rashba spin-orbit interaction. A qualitative agreement with experimental data is found regarding the satellite peaks. The spin polarization is predicted to be larger than ten percent for magnetic fields above 2 Tesla and having a structure even at the satellite peaks. The Rashba effect is confirmed to be observable as a beating pattern in the density of states but found to be too small to affect the tunnelling current.Comment: 31 pages, 11 figure