Designing predefined-time differentiators with bounded time-varying gains

There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies are either only available for first-order differentiators, yielding a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST

The Theory of Functional Forms of the Consumer Demand System and its Application

This dissertation studies the consumer demand system focusing on its functional forms in the theoretical aspect and the empirical aspect. The theoretical part investigates the regularity property of the consumer demand system with the normalized quadratic functional form. We display the regular regions of the model whose parameters are estimated using different methods of imposing curvature. We find that the model often violates the monotonicity condition regardless of how curvature is imposed. The empirical part applies functional forms of the consumer demand system which are flexible in the total expenditure in estimating the cost of children using Japanese household expenditure data. We find that the cost of additional child is higher for poor households than for rich households. This suggests that the child-support program being proposed by the Japanese government should have a mechanism to decrease the benefit as household income increases

Identifying, measuring and management risks in Russian secondary stock markets

: This paper outlines the changes and challenges of Emerging Russian Stock Market and investment strategy of portfolio management for the period 1996-1998 . It also taste the West models of optimization of portfolio risks and investment decisions for Russia. The major purpose of this article was to enhance the understanding of the participants in securities markets and enhance the performance of its stock and Emerging securities. This article will review the trends in the markets and help focus on the corporate risks and management and a detailed and developed conception of the mechanism of the initial public offerings and public placement of securities the global stock markets such as the U.S., Western Europe and emerging markets. It also outlined the regulatory structure and investor?s risk management tools required by western investors. In light of the recent ?financial crisis? in Russia and other major markets such as Asia, these tools will be increasing important. During much of the past decade the Russian Securities market has been developing into a number of areas including federal securities (GKO-OFZ), sub-federal (oblast) and municipal issues, corporate securities, Ag Bonds, futures, forward contracts and currency instruments. This article is developing in all those areasm .These will be increasing important in light of the new banking environment and securities laws and regulations. In 1997 Russia has joined the league of the few emerging markets that have market capitalizations of over $100 Billion. As of June 30, 1997 the capitalization is$104 Billion and has a YTD of 134 %. The recent ?Asian induced? corrections in the markets have reduced this by 20-40% according to private estimates. Nevertheless, it remains one of the most vibrant emerging securities markets in the world. The training focused on a number of issues related to emerging market securities including privatization, auctions, IPO?s and new products in the securities markets.

Probabilistic Modeling, Estimation and Control for CALS Organization-Technical-Economic Systems

Theoretical propositions of new probabilistic methodology of analysis, modeling, estimation and control in stochastic organizational-technical-economic systems (OTES) based on stochastic CALS informational technologies are considered. Stochastic integrated logistic support (ILS) of OTES modeling life cycle (LC), stochastic optimal of current state estimation in stochastic media defined by internal and external noises (including specially organized OTES-NS (noise support) and stochastic OTES optimal control) according to social-technical-economic-support criteria in real time by informational-analytical tools (IAT) of global type are presented. OTES-CALS are nonlinear and continuous-discrete. So we use approximate methods of normal approximation of probabilistic densities both for modeling and estimation. Spectrum of possibilities may be broaden by solving problems of OTES-CALS integration for existing markets of finances, goods and services. Analytical modeling, analysis, parametric optimization and optimal stochastic processes regulation in limits of illustrate some technologies and IAT given plans

Task Specific Uncertainty in Coordinate Measurement

Task specific uncertainty is the measurement uncertainty associated with the measurement of a specific feature using a specific measurement plan. This paper surveys techniques developed to model and estimate task specific uncertainty for coordinate measuring systems, primarily coordinate measuring machines using contacting probes. Sources of uncertainty are also reviewed

Convex Relaxation of Optimal Power Flow, Part II: Exactness

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, June 2014. This is an extended version with Appendex VI that proves the main results in this tutoria

Estimating fuel consumption from radar tracks

Fuel consumption is one of the major considerations for both the impact of aviation in the environment and the cost of operations. This paper assesses the accuracy of a method capable of producing aircraft fuel estimates based on their 4D trajectory and the weather forecast. Fuel consumption estimates generated for 2448 descents are compared with the flight data recorder (FDR) values provided by the airline. Fuel consumption is estimated by taking the 4D trajectory from two different sources: the FDR system itself and surveillance radar tracks. In both cases, the Base of Aircraft Data (BADA) and a model that fits manufacturers’ performance data to polynomial functions are used to represent aircraft performance. Results obtained with the later show that fuel usage could be estimated with an accuracy of 16 kg (4.8%) by using the 4D trajectory as reported by the FDR system and 28 kg (7.8%) by using surveillance radar observations. It is also observed that the BADA 3.6 model underestimates the fuel consumption, illustrating the need for an improved performance model in the terminal manoeuvring area.Peer ReviewedPostprint (published version

Message Passing for Integrating and Assessing Renewable Generation in a Redundant Power Grid

A simplified model of a redundant power grid is used to study integration of fluctuating renewable generation. The grid consists of large number of generator and consumer nodes. The net power consumption is determined by the difference between the gross consumption and the level of renewable generation. The gross consumption is drawn from a narrow distribution representing the predictability of aggregated loads, and we consider two different distributions representing wind and solar resources. Each generator is connected to D consumers, and redundancy is built in by connecting R of these consumers to other generators. The lines are switchable so that at any instance each consumer is connected to a single generator. We explore the capacity of the renewable generation by determining the level of "firm" generation capacity that can be displaced for different levels of redundancy R. We also develop message-passing control algorithm for finding switch settings where no generator is overloaded.Comment: 10 pages, accepted for HICSS-4