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

Effects of local event-by-event conservation laws in ultrarelativistic heavy-ion collisions at particlization

Many simulations of relativistic heavy-ion collisions involve the switching from relativistic hydrodynamics to kinetic particle transport. This switching entails the sampling of particles from the distribution of energy, momentum, and conserved currents provided by hydrodynamics. Usually, this sampling ensures the conservation of these quantities only on the average, i.e., the conserved quantities may actually fluctuate among the sampled particle configurations and only their averages over many such configurations agree with their values from hydrodynamics. Here we apply a recently invented method [D. Oliinychenko and V. Koch, Phys. Rev. Lett. 123, 182302 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.182302] to ensure conservation laws for each sampled configuration in spatially compact regions (patches) and study their effects: From the well-known (micro-)canonical suppression of means and variances to little studied (micro-)canonical correlations and higher-order fluctuations. Most of these effects are sensitive to the patch size. Many of them do not disappear even in the thermodynamic limit, when the patch size goes to infinity. The developed method is essential for particlization of stochastic hydrodynamics. It is useful for studying the chiral magnetic effect, small systems, and in general for fluctuation and correlation observables

Drastic improvement of surface structure and current-carrying ability in YBa2Cu3O7 films by introducing multilayered structure

Much smoother surfaces and significantly improved superconducting properties of relatively thick YBa2Cu3O7 (YBCO) films have been achieved by introducing a multilayered structure with alternating main YBCO and additional NdBCO layers. The surface of thick (1 microm) multilayers has almost no holes compared to YBCO films. Critical current density (Jc) have been drastically increased up to a factor > 3 in 1 microm multilayered structures compared to YBCO films over entire temperature and applied magnetic filed range. Moreover, Jc values measured in thick multilayers are even larger than in much thinner YBCO films. The Jc and surface improvement have been analysed and attributed to growth conditions and corresponding structural peculiarities.Comment: Accepted to Appl. Phys. Lett. 88, June (2006), in press 4 pages, 3 figure

Mixed integer nonlinear programming for Joint Coordination of Plug-in Electrical Vehicles Charging and Smart Grid Operations

The problem of joint coordination of plug-in electric vehicles (PEVs) charging and grid power control is to minimize both PEVs charging cost and energy generation cost while meeting both residential and PEVs' power demands and suppressing the potential impact of PEVs integration. A bang-bang PEV charging strategy is adopted to exploit its simple online implementation, which requires computation of a mixed integer nonlinear programming problem (MINP) in binary variables of the PEV charging strategy and continuous variables of the grid voltages. A new solver for this MINP is proposed. Its efficiency is shown by numerical simulations.Comment: arXiv admin note: substantial text overlap with arXiv:1802.0445

Sparse Bilinear Logistic Regression

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.Comment: 27 pages, 5 figure

Construction of a high-resolution genetic linkage map and comparative genome analysis for the reef-building coral Acropora millepora

Section of Integrative Biology, School of Biological Sciences, University of Texas at Austin, 1 University Station C0930, Austin, TX 78712, USABackground: Worldwide, coral reefs are in decline due to a range of anthropogenic disturbances, and are now also under threat from global climate change. Virtually nothing is currently known about the genetic factors that might determine whether corals adapt to the changing climate or continue to decline. Quantitative genetics studies aiming to identify the adaptively important genomic loci will require a high-resolution genetic linkage map. The phylogenetic position of corals also suggests important applications for a coral genetic map in studies of ancestral metazoan genome architecture. Results: We constructed a high-resolution genetic linkage map for the reef-building coral Acropora millepora, the first genetic map reported for any coral, or any non-Bilaterian animal. More than 500 single nucleotide polymorphism (SNP) markers were developed, most of which are transferable in populations from Orpheus Island and Great Keppel Island. The map contains 429 markers (393 gene-based SNPs and 36 microsatellites) distributed in 14 linkage groups, and spans 1,493 cM with an average marker interval of 3.4 cM. Sex differences in recombination were observed in a few linkage groups, which may be caused by haploid selection. Comparison of the coral map with other metazoan genomes (human, nematode, fly, anemone and placozoan) revealed synteny regions. Conclusions: Our study develops a framework that will be essential for future studies of adaptation in coral and it also provides an important resource for future genome sequence assembly and for comparative genomics studies on the evolution of metazoan genome structure.Integrative [email protected]