Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control

Hybrid systems: a real-time interface to control engineering

This paper gives an introduction to a general hybrid systems model for definition of system requirements and a corresponding software architecture together with an example of their specialization for use in implementing a modeswitching controller for a hydraulic cylinder. 1. Introduction An important application area for real-time computing is embedded systems where the computing system provides intelligent control of a mechanical, chemical etc. plant or device. The software requirements for such applications depend heavily on the properties of the plant. These properties are usually investigated by control engineers that base their work on the theory of dynamic systems [3, 9]. The mathematical tool for this work is thus mathematical analysis, in particular the theory of differential equations. If the models are linear differential equations, there are standard techniques for implementing a corresponding discrete, sampled system in the form of a computer program, and the work for the s..

Informació i control en educació matemàtica

En este artículo se analizan dos aspectos clave de la educación matemática: los procesos de información y de control en el marco de la teoria de la instrucción. El artículo se estructura en los siguientes puntos: 1. Introducción: la educación matemática, las variables instructivas y el constructivismo como modelo epistemológico y psicológico. 2. Implementación: acciones, gestión y decisiones. 3. Eficiencia: observación, autorreflexión y evaluación-recursión.In this article we analyse two key aspects of the mathematical education: the processes of information and control within the framework of the theory of instruction. The article is structured as follows: 1. Introduction: mathematical education, instructive variables and constructivism as an epistemological and psycological model. 2. Implementation: actions, management and decisions. 3. Efficiency: observation, selfreflection and evaluation

Proposals for a basic theory of air traffic control

This note serves as an introduction to the work on Air Traffic Control currently being carried out at The College of Aeronautics. The basic principles of Air Traffic Control are examined and a mathematical basis for an analysis of the current and future ATC complex is discussed. The theory is based upon feedback control concepts using intermittent data. Examples showing the application to en-route airway and parallel track flying are given. These demonstrate the effect of positional data up-dating rate upon separation minima for both subsonic and supersonic aircraft. Application to both fixed route (Airway Control) and free-route (Area Control) are currently being considered. A full report is to be published at a later date

Informational aspects of the haptic stimulation by the light for correction of the human functional state

Introduction. The study of the laws and principles of information processes in the biological systems of the human body in extreme forms of its activities and the development of the theory of medical information systems of such appointment, taking into account the status and trends of convergence of society, ecosystems and technology become very relevant. This state of affairs makes it possible to affirm that it is an actual scientific and applied problem of radical change of the existing paradigm of designing information systems. The purpose of the article is to specify the informational aspects of low intensity, haptic stimulation by the light, which is essential for correction of the functional state of an organism of the human being, who works in extreme conditions, to develop and study such methods and systems. Methods. Analyses of requirements, functions and systems for designing synthesis of information technologies and the control biotechnical system of correction of the functional state of an organism of the human, who works in extreme conditions. The theoretical and experimental dependences between the stimulation energy of light emission diode (LED) and the energy are transferred through the layered bio media design. Mathematical modelling and computational simulation. Comparison of these real and model data. Results. The base aspects requirements, functions and systems for designing synthesis of information technologies and the control biotechnical system of correction of the functional state of an organism of the human, who works in extreme conditions, low intensity, haptic stimulation by the light are defined. The methods for determining of intensity I0 of light emission diode, recursive expression , and formula for coefficient Cm , where M — quantity of bio media layers were developed. The bridges, which connects Maxwell’s phenomenological theory with the atomistic theory of matter and optics, were used. Computer simulation studies have confirmed the specification of requirements, functional and structural schemas of biotechnical system. Conclusions. Thanking to specification of requirements possibility-using recursive determining of the light flux intensity after every bio media layer was got. Under the effect of recurstion low computation complexity was caused. Information technology means (for automation optimal control) of the human state under external influences on the organism was developed. Further study to confirm statistical significance in representative samples of observations was opened

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion

Introducing Anthropological Foundations of Economic Behavior, Organization, and Control

One of the rude awakenings for economists from the current recession is an emerging understanding that economics has gone wild with its highbrow mathematical models that bear little resemblance to reality. The failure of economics to predict and solve the current global recession, has restored the “dismal science” title to the profession. It stems from the cultish fascination with Adam Smith’s Invisible Hand, centered around the belief in the efficient market hypothesis. This fascination exposes analytical holes in the methodology that economics has followed lately, as economics itself has moved too far away from its key social foundations. This situation is incomprehensible and needs redressing. I compiled a book - Selected Readings on the Anthropological Bases of Economic Behavior, Organization, and Control - to help economists and others get back in touch with their genealogy. This current paper is a watered down version of the introduction to Selected Readings. It concludes that real life is neither as simple nor economic as economic theory sometimes suggests. In fact, and for much of human history, non-economic factors and forces have driven economic activities. Selected Readings provides an opportunity for reinforced focus on economics principles. Alone and detached from its social foundations economics has a future only as fiction. As serious non-fiction, economics cannot successfully divorce itself from its elemental foundations in the social sciences. To advance its theory in the past economics needed to borrow from mathematics and physics. Such learning must continue. However, to remain policy-relevant economics cannot wish away the very social bases upon which it is founded. Without social foundations one might as well kiss economics goodbye.economic behavior, economic organization, economic control, Frank Knight, W. Arthur Lewis, Joan Robinson, Janos Kornai, J. Herskovits, B. Malinowski, anthropological bases