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

Hiding dark energy transitions at low redshift

We show that it is both observationally allowable and theoretically possible to have large fluctuations in the dark energy equation of state as long as they occur at ultra-low redshifts z<0.02. These fluctuations would masquerade as a local transition in the Hubble rate of a few percent or less and escape even future, high precision, high redshift measurements of the expansion history and structure. Scalar field models that exhibit this behavior have a sharp feature in the potential that the field traverses within a fraction of an e-fold of the present. The equation of state parameter can become arbitrarily large if a sharp dip or bump in the potential causes the kinetic and potential energy of the field to both be large and have opposite sign. While canonical scalar field models can decrease the expansion rate at low redshift, increasing the local expansion rate requires a non-canonical kinetic term for the scalar field.Comment: 4 pages, 2 figures; submitted to Phys. Rev. D (Brief Report

JAPANESE IMPORT DEMAND FOR U.S. BEEF AND PORK: EFFECTS ON U.S. RED MEAT EXPORTS AND LIVESTOCK PRICES

Japanese import demand for U.S. beef and pork products and the effects on domestic livestock prices are econometrically estimated. Japan is the most important export market for U.S. beef and pork products. Results indicate foreign income, exchange rates, and protectionist measures are statistically significant. The comparative statistics quantify the effects of recent economic volatility. For example, the 1995-1998 depreciation in the Japanese yen (39%) reduced U.S. slaughter steer and hog prices by $1.29 per cwt and$0.99 per cwt, respectively, while the 1994-1998 reduction in tariffs (14%) increased slaughter steer and hog prices by $0.49 per cwt and$0.33 per cwt, respectively. Livestock producers will continue to have a vested interest in Asian trade liberalization policies.elasticities, exchange rates, import demand, income, tariffs, Demand and Price Analysis, Q17, F14, C32,

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant

Towards automated design of quantum cascade lasers

We present an advanced technique for the design and optimization of GaAs/AlGaAs quantum cascade laser structures. It is based on the implementation of the simulated annealing algorithm with the purpose of determining a set of design parameters that satisfy predefined conditions, leading to an enhancement of the device output characteristics. Two important design aspects have been addressed: improved thermal behavior, achieved by the use of higher conduction band offset materials, and a more efficient extraction mechanism, realized via a ladder of three lower laser states, with subsequent pairs separated by the optical phonon energy. A detailed analysis of performance of the obtained structures is carried out within a full self-consistent rate equations model of the carrier dynamics. The latter uses wave functions calculated by the transfer matrix method, and evaluates all relevant carrier–phonon and carrier–carrier scattering rates from each quantized state to all others within the same and neighboring periods of the cascade. These values are then used to form a set of rate equations for the carrier density in each state, enabling further calculation of the current density and gain as a function of the applied field and temperature. This paper addresses the application of the described procedure to the design of lambda~9 µm GaAs-based mid-infrared quantum cascade lasers and presents the output characteristics of some of the designed optimized structures. © 2005 American Institute of Physic

Artificial intelligence techniques for flood risk management in urban environments

Open Access journalCopyright © 2013 The Authors. Published by Elsevier Ltd.12th International Conference on Computing and Control for the Water Industry, CCWI2013Urban flooding is estimated to cause £270 million pounds worth of damage each year in England and Wales alone. There has, therefore, been a clear need to develop improved methods of identifying intervention strategies to reduce flood risk in urban environments. This paper describes ground-work performed towards evaluating the relative suitability of several algorithms applied to multi-objective optimisation of flood risk intervention strategies in an urban drainage network. An effective methodology is described for reducing an array of return period/duration rainfall files to a minimum, and it is described how this methodology makes possible comparisons of optimisation algorithms. This work has been undertaken as part of a STREAM-IDC EngD project which is a collaborative effort between the University of Exeter, and HR Wallingford

Settling Time Optimization in Wire Bonder Systems Via Extremum-Seeking Control

Adequate tuning of control laws is essential for high positioning accuracy, large system throughput, and reliability in high-end mechatronic and robotic systems. However, a population of such systems generally shows slight variations in dynamic responses due to, e.g., manufacturing tolerances, different disturbance situations, or position-dependent dynamics. Given the time-consuming nature of controller design, even by experienced control engineers, typically just one control law is designed for the whole system population based on worst-case bounds on variations in dynamic responses, resulting in a loss of individual system performance. The main contribution of this paper is the development of an automated controller tuning approach, based on extremum-seeking control, for settling time optimization via individual controller tuning. While other automated controller tuning methods exist, the developed approach allows inclusion of closed-loop stability and robustness constraints based solely on non-parametric frequency-response measurements of open-loop plant dynamics, and therewith directly optimizes transient system performance in a purely data-based manner. The proposed approach has been applied in simulation in an industrial case study for settling time optimization in point-to-point motions of a wire bonder system. In this case study, the effectiveness of the approach has been shown by achieving significant performance increases of 39.4% and 40.6% compared to controllers designed by experienced control engineers using manual loop-shaping techniques and a frequency-based auto-tuner, respectively, without needing manual tuning effort

Density matrix theory of transport and gain in quantum cascade lasers in a magnetic field

A density matrix theory of electron transport and optical gain in quantum cascade lasers in an external magnetic field is formulated. Starting from a general quantum kinetic treatment, we describe the intraperiod and interperiod electron dynamics at the non-Markovian, Markovian, and Boltzmann approximation levels. Interactions of electrons with longitudinal optical phonons and classical light fields are included in the present description. The non-Markovian calculation for a prototype structure reveals a significantly different gain spectra in terms of linewidth and additional polaronic features in comparison to the Markovian and Boltzmann ones. Despite strongly controversial interpretations of the origin of the transport processes in the non- Markovian or Markovian and the Boltzmann approaches, they yield comparable values of the current densities

A few provoking relations between dark energy, dark matter and pions

I present three relations, striking in their simplicity and fundamental appearance. The first one connects the Compton wavelength of a pion and the dark energy density of the Universe; the second one connects Compton wavelength of a pion and the mass distribution of non-baryonic dark matter in a Galaxy; the third one relates mass of a pion to fundamental physical constants and cosmological parameters. All these relations are in excellent numerical agreement with observations