DOCSLIB.ORG

Nonlinear and Quantitative Software Engineering Method Based on Complexity Science

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Nonlinear and Quantitative Software Engineering Method Based on Complexity Science Recent Advances in Computer Science Nonlinear and Quantitative Software Engineering Method Based on Complexity Science Jay Xiong Lin Li NSEsoftware, LLC., USA www.nsesoftware.com [email protected] [email protected] Abstract—This paper introduces a nonlinear and quantitative software engineering method (NSE-Method), which is the core part of the Nonlinear Software Engineering paradigm (NSE) based on complexity science. NSE-Method offers a nonlinear, holistic, global, and quantitative approach for software development. The objective of NSE-Method is to make it possible to help software development organizations double their productivity, halve their cost, and improve the quality of their software products by several orders of magnitude simultaneously. NSE-Method has been successfully implemented and supported by the NSE platform, Panorama++, integrated from many automated software engineering tools. Keywords: Software engineering method; complexity science; nonlinear software engineering; software engineering paradigm (a) Incomplete – the process is incomplete: “The Unified I. INTRODUCTION Process suffers from several weaknesses. First, it is only a Today software has become the driving force for the development process… it misses the concept of maintenance development of all kinds of sciences, engineering, and and support…. The relative software investment that most businesses. As pointed out by David Rice, “Like cement, organizations make is allocating roughly 20% of the software software is everywhere in modern civilization. Software is in budget for new development, and 80% to maintenance and your mobile phone, in your home computer, in cars, airplanes, support efforts.” （Scott Ambler, [2]). In fact not only RUP, hospitals, businesses, public utilities, financial systems, and but almost all existing software development methods do not national defense systems. " [1] really support software maintenance without various bi- But unfortunately, software itself is not well engineered, directional traceabilities. many critical issues (low quality and productivity, and high (b) Inconsistent - the design documents and the source cost and risk, etc.) have existed with software development for code of a software product developed using existing methods more than 50 years. are inconsistent with each other after code modification again The root cause is that software is a nonlinear system where and again. a small change may bring big impacts to the entire system – the (c) Unreliable - “Major software projects have been “Butterfly-Effect” — but the old-established software troubling business activities for more than 50 years. Of any engineering paradigm with all existing software development known business activity, software projects have the highest methods is an outcome of linear thinking, reductionism, and the probability of being cancelled or delayed. Once delivered, these superposition principle that the whole of a nonlinear system is projects display excessive error quantities and low levels of the sum of its parts, so that with it almost all software reliability.” (Capers Jones, [3]). This is why software disasters engineering activities are performed linearly, partially, locally, happen often. and qualitatively. (d) Un-maintainable - “Over three decades ago, software For efficiently resolving those critical issues, a new maintenance was characterized as an ‘iceberg’. We hope that software engineering method called NSE-Method has been what is immediately visible is all there is to it, but we know innovated which complies with the essential principles of that an enormous mass of potential problems and cost lies complexity science. Theoretical comparison with initial under the surface. In the early 1970s, the maintenance iceberg applications shows that compared with the old software was big enough to sink an aircraft carrier. Today, it could engineering methods it is possible for NSE-Method and the easily sink the entire navy!” (Roger S. Pressman, [4]). “The corresponding tools to help software development fundamental problem with program maintenance is that fixing organizations double their productivity, halve their cost, and a defect has a substantial (20–50%) chance of introducing improve the quality of their software products by several orders another”(Brooks, [5]). This is why so many cloud computing of magnitude simultaneously. system failures were reported in 2011, including * Sony’s Playstation Network (4/21/2011) II. CRITICAL ISSUES ADDRESSED * Amazon Web Services (4/21/2011) The critical issues addressed by NSE-Method have existed * Twitter Service (2/25/2011) with software development for more than 50 years, including * Netflix Streaming Service (3/22/2011) ISBN: 978-960-474-311-7 276 Recent Advances in Computer Science * Intuit Service and Quickbooks (3/28/2011), and more [6]. (e) Invisible – the existing visualization methods, techniques, and tools do not offer the capability to make the entire software development process and the work products visible; in most cases, the generated charts and diagrams are used for modeling only, and are not holistic and not traceable. (f) More – there are more critical issues existing with software development, including low quality and productivity, high cost and risk, etc. Fig. 2 Linear software engineering methods III. WHY HAVE THOSE CRITICAL ISSUES EXISTED FOR MORE (Source: “An Analysis of Model Driven Architecture (MDA) and THAN 50 YEARS WITHOUT BEING RESOLVED? Executable UML (xUML)”, http://www.powershow.com/view/30871- As we know well, many software engineering methods and MjU5N/An_Analysis_of_Model_Driven_Architecture_MDA_and_Exec utable_UML_xUML_flash_ppt_presentation ) technologies have been innovated and applied by software scientists, experts, and engineers such as the Object-Oriented software development approach, the platform-independent Java programming language, the model-driven software Fig. 3 Software development methods based on the development methods, and the Agile software development Constructive Holism Principle approaches, but why those critical issues have existed for more than 50 years without being resolved? (b) The existing software modeling approaches - they are Before answering this question, let us consider what makes outcomes of reductionism and the superposition those critical issues exist: principle, which use different sources for human (a) The process models – they are linear ones, no matter if understanding and computer understanding of a it is a waterfall-like model, an incremental development software system separately, with a big gap between “ ” model which is a series of Waterfalls , or an iterative them as shown in Fig. 4. The resulting models are not development model in which each time of the iteration is a traceable for static defect removal, not executable for waterfall, or a new process model recommended by debugging, and not testable for dynamic defect Alistair Cockburn to combine both Incremental and removal, not consistent with the source code, and not Iterative development together [7] shown in Fig. 1, with qualified as the road map for software development - which there is no upstream movement at all, the work nobody knows whether they are complete or not, flow is always going forward from the upper phases to the correct or not, and consistent with each other or not. lower phases. The result is that defects introduced in the We hope the next generation of UML and the upper phases easily propagate to the lower phases to make MDA/MDD/MDE can solve those problems. the defect removal cost increase as much as tenfold. Fig. 1 “Putting Iterative and Incremental Development Together” (b) The software development methods – as shown in Fig. 2, Fig. 4 The existing software modeling approaches they are one-way software development methods (Top- Down or Bottom-Up) based on linear thinking, (c) The software testing paradigm – most software reductionism, and Constructive Holism principle that the defects are introduced into a software product in the software components are developed first, then the system requirement development phase and the product design of a software product is built through the integration of phase as shown in Fig. 5, but the existing software the components developed (see Fig. 3) - “Assemble the testing paradigm can only be dynamically used after product from the product components, ensure the production as shown in Fig. 6 and Fig. 7, so that NIST product, as integrated, functions properly and deliver the (National Institute of Standards and Technology) product.” [8] , so that system testing is performed after concluded that “Briefly, experience in testing software all components have been developed. With these and systems has shown that testing to high degrees of methods, the quality of a software product is carried out security and reliability is from a practical perspective through inspection and software testing after production – not possible. Thus, one needs to build security, it is too late. reliability, and other aspects into the system design itself and perform a security fault analysis on the ISBN: 978-960-474-311-7 277 Recent Advances in Computer Science implementation of the design.” (("Requiring Software or more projects being developed, it is hard to balance Independence in VVSG 2007: STS the development. Recommendations for the TGDC," November 2006, (j) The entire software engineering paradigm - it is an http://vote.nist.gov/DraftWhitePaperOnSIinVVSG2007 outcome of linear thinking, reductionism, and
Load more

Recommended publications
  • Coping with the Bounds: a Neo-Clausewitzean Primer / Thomas J
    About the CCRP The Command and Control Research Program (CCRP) has the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: • articulating critical research issues; • working to strengthen command and control research infrastructure; • sponsoring a series of workshops and symposia; • serving as a clearing house for command and control related research funding; and • disseminating outreach initiatives that include the CCRP Publication Series. This is a continuation in the series of publications produced by the Center for Advanced Concepts and Technology (ACT), which was created as a “skunk works” with funding provided by the CCRP under the auspices of the Assistant Secretary of Defense (NII). This program has demonstrated the importance of having a research program focused on the national security implications of the Information Age. It develops the theoretical foundations to provide DoD with information superiority and highlights the importance of active outreach and dissemination initiatives designed to acquaint senior military personnel and civilians with these emerging issues.
    [Show full text]
  • Observation of Nonlinear Verticum-Type Systems Applied to Ecological Monitoring
    2nd Reading June 4, 2012 13:53 WSPC S1793-5245 242-IJB 1250051 International Journal of Biomathematics Vol. 5, No. 6 (November 2012) 1250051 (15 pages) c World Scientific Publishing Company DOI: 10.1142/S1793524512500519 OBSERVATION OF NONLINEAR VERTICUM-TYPE SYSTEMS APPLIED TO ECOLOGICAL MONITORING S. MOLNAR´ Institute of Mathematics and Informatics Szent Istv´an University P´ater K. u. 1., H-2103 Godollo, Hungary [email protected] M. GAMEZ´ ∗ and I. LOPEZ´ † Department of Statistics and Applied Mathematics University of Almer´ıa La Ca˜nada de San Urbano 04120 Almer´ıa, Spain ∗[email protected] †[email protected] Received 4 November 2011 Accepted 13 January 2012 Published 7 June 2012 In this paper the concept of a nonlinear verticum-type observation system is introduced. These systems are composed from several “subsystems” connected sequentially in a particular way: a part of the state variables of each “subsystem” also appears in the next “subsystem” as an “exogenous variable” which can also be interpreted as a con- trol generated by an “exosystem”. Therefore, these “subsystems” are not observation systems, but formally can be considered as control-observation systems. The problem of observability of such systems can be reduced to rank conditions on the “subsystems”. Indeed, under the condition of Lyapunov stability of an equilibrium of the “large”, verticum-type system, it is shown that the Kalman rank condition on the linearization of the “subsystems” implies the observability of the original, nonlinear verticum-type system. For an illustration of the above linearization result, a stage-structured fishery model with reserve area is considered.
    [Show full text]
  • Nonlinear System Stability and Behavioral Analysis for Effective
    S S symmetry Article Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb Susmita Das 1 , Dalia Nandi 2, Biswarup Neogi 3 and Biswajit Sarkar 4,* 1 Narula Institute of Technology, Kolkata 700109, India; [email protected] 2 Indian Institute of Information Technology Kalyani, Kalyani 741235, India; [email protected] 3 JIS College of Engineering., Kalyani 741235, India; [email protected] 4 Department of Industrial Engineering, Yonsei University, Seoul 03722, Korea * Correspondence: [email protected] or [email protected] Received: 8 September 2020; Accepted: 14 October 2020; Published: 19 October 2020 Abstract: System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems.
    [Show full text]
  • Spectral Properties of the Koopman Operator in the Analysis of Nonstationary Dynamical Systems
    UNIVERSITY of CALIFORNIA Santa Barbara Spectral Properties of the Koopman Operator in the Analysis of Nonstationary Dynamical Systems A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering by Ryan M. Mohr Committee in charge: Professor Igor Mezi´c,Chair Professor Bassam Bamieh Professor Jeffrey Moehlis Professor Mihai Putinar June 2014 The dissertation of Ryan M. Mohr is approved: Bassam Bamieh Jeffrey Moehlis Mihai Putinar Igor Mezi´c,Committee Chair May 2014 Spectral Properties of the Koopman Operator in the Analysis of Nonstationary Dynamical Systems Copyright c 2014 by Ryan M. Mohr iii To my family and dear friends iv Acknowledgements Above all, I would like to thank my family, my parents Beth and Jim, and brothers Brennan and Gralan. Without their support, encouragement, confidence and love, I would not be the person I am today. I am also grateful to my advisor, Professor Igor Mezi´c,who introduced and guided me through the field of dynamical systems and encouraged my mathematical pursuits, even when I fell down the (many) proverbial (mathematical) rabbit holes. I learned many fascinating things from these wandering forays on a wide range of topics, both contributing to my dissertation and not. Our many interesting discussions on math- ematics, research, and philosophy are among the highlights of my graduate school career. His confidence in my abilities and research has been a constant source of encouragement, especially when I felt uncertain in them myself. His enthusiasm for science and deep, meaningful work has set the tone for the rest of my career and taught me the level of research problems I should consider and the quality I should strive for.
    [Show full text]
  • Rethinking the International System As a Complex Adaptive System
    Munich Personal RePEc Archive A New Taxonomy for International Relations: Rethinking the International System as a Complex Adaptive System Scartozzi, Cesare M. University of Tokyo, Graduate School of Public Policy 2018 Online at https://mpra.ub.uni-muenchen.de/95496/ MPRA Paper No. 95496, posted 12 Aug 2019 10:50 UTC 1SFQVCMJDBUJPOJournal on Policy and Complex Systems • Volume 4, Number 1 • Spring 2018 A New Taxonomy for International Relations: Rethinking the International System as a Complex Adaptive System Cesare Scartozzi Graduate School of Public Policy, University of Tokyo [email protected] 7-3-1, Hongo, Bunkyo, Tokyo 113-0033, Japan ORCID number: 0000-0002-4350-4386. Abstract The international system is a complex adaptive system with emer- gent properties and dynamics of self-organization and informa- tion processing. As such, it is better understood with a multidis- ciplinary approach that borrows methodologies from the field of complexity science and integrates them to the theoretical perspec- tives offered by the field of international relations (IR). This study is set to formalize a complex systems theory approach to the study of international affairs and introduce a new taxonomy for IR with the two-pronged aim of improving interoperability between differ- ent epistemological communities and outlining a formal grammar that set the basis for modeling international politics as a complex adaptive system. Keywords: international politics, international relations theory, complex systems theory, taxonomy, adaptation, fitness, self-orga- nization This is a prepublication version of: Scartozzi, Cesare M. “A New Taxonomy for International Relations: Rethinking the International System as a Complex Adaptive System.” Journal on Policy and Complex Systems 4, no.
    [Show full text]
  • Chapter 8 Nonlinear Systems
    Chapter 8 Nonlinear systems 8.1 Linearization, critical points, and equilibria Note: 1 lecture, §6.1–§6.2 in [EP], §9.2–§9.3 in [BD] Except for a few brief detours in chapter 1, we considered mostly linear equations. Linear equations suffice in many applications, but in reality most phenomena require nonlinear equations. Nonlinear equations, however, are notoriously more difficult to understand than linear ones, and many strange new phenomena appear when we allow our equations to be nonlinear. Not to worry, we did not waste all this time studying linear equations. Nonlinear equations can often be approximated by linear ones if we only need a solution “locally,” for example, only for a short period of time, or only for certain parameters. Understanding linear equations can also give us qualitative understanding about a more general nonlinear problem. The idea is similar to what you did in calculus in trying to approximate a function by a line with the right slope. In § 2.4 we looked at the pendulum of length L. The goal was to solve for the angle θ(t) as a function of the time t. The equation for the setup is the nonlinear equation L g θ�� + sinθ=0. θ L Instead of solving this equation, we solved the rather easier linear equation g θ�� + θ=0. L While the solution to the linear equation is not exactly what we were looking for, it is rather close to the original, as long as the angleθ is small and the time period involved is short. You might ask: Why don’t we just solve the nonlinear problem? Well, it might be very difficult, impractical, or impossible to solve analytically, depending on the equation in question.
    [Show full text]
  • NONLINEARITIES, FEEDBACKS and CRITICAL THRESHOLDS WITHIN the EARTH's CLIMATE SYSTEM 1. Introduction Nonlinear Phenomena Charac
    NONLINEARITIES, FEEDBACKS AND CRITICAL THRESHOLDS WITHIN THE EARTH’S CLIMATE SYSTEM JOSÉ A. RIAL 1,ROGERA.PIELKESR.2, MARTIN BENISTON 3, MARTIN CLAUSSEN 4, JOSEP CANADELL 5, PETER COX 6, HERMANN HELD 4, NATHALIE DE NOBLET-DUCOUDRÉ 7, RONALD PRINN 8, JAMES F. REYNOLDS 9 and JOSÉ D. SALAS 10 1Wave Propagation Laboratory, Department of Geological Sciences CB#3315, University of North Carolina, Chapel Hill, NC 27599-3315, U.S.A. E-mail: [email protected] 2Atmospheric Science Dept., Colorado State University, Fort Collins, CO 80523, U.S.A. 3Dept. of Geosciences, Geography, Univ. of Fribourg, Pérolles, Ch-1700 Fribourg, Switzerland 4Potsdam Institute for Climate Impact Research, Telegrafenberg C4, 14473 Potsdam, P.O. Box 601203, Potsdam, Germany 5GCP-IPO, Earth Observation Centre, CSIRO, GPO Box 3023, Canberra, ACT 2601, Australia 6Met Office Hadley Centre, London Road, Bracknell, Berkshire RG12 2SY, U.K. 7DSM/LSCE, Laboratoire des Sciences du Climat et de l’Environnement, Unité mixte de Recherche CEA-CNRS, Bat. 709 Orme des Merisiers, 91191 Gif-sur-Yvette, France 8Dept. of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. 9Department of Biology and Nicholas School of the Environmental and Earth Sciences, Phytotron Bldg., Science Dr., Box 90340, Duke University, Durham, NC 27708, U.S.A. 10Dept. of Civil Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A. Abstract. The Earth’s climate system is highly nonlinear: inputs and outputs are not proportional, change is often episodic and abrupt, rather than slow and gradual, and multiple equilibria are the norm.
    [Show full text]
  • Modeling Vascular Homeostasis and Improving Data Filtering Methods for Model Calibration
    Modeling Vascular Homeostasis and Improving Data Filtering Methods for Model Calibration by Jiacheng Wu A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering − Mechanical Engineering and the Designated Emphasis in Computational Science and Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Shawn C. Shadden, Chair Professor Grace D. O'Connell Professor Peter L. Bartlett Spring 2019 Modeling Vascular Homeostasis and Improving Data Filtering Methods for Model Calibration Copyright 2019 by Jiacheng Wu 1 Abstract Modeling Vascular Homeostasis and Improving Data Filtering Methods for Model Calibration by Jiacheng Wu Doctor of Philosophy in Engineering − Mechanical Engineering and the Designated Emphasis in Computational Science and Engineering University of California, Berkeley Professor Shawn C. Shadden, Chair Vascular homeostasis is the preferred state that blood vessels try to maintain against external mechanical and chemical stimuli. The vascular adaptive behavior around the homeostatic state is closely related to cardiovascular disease progressions such as arterial aneurysms. In this work, we develop a multi-physics computational framework that couples vascular growth & remodeling (G&R), wall mechanics and hemodynamics to describe the overall vascular adaptive behavior. The coupled simulation is implemented in patient-specific geometries to predict aneurysm progression. Lyapunov stability analysis of the governing
    [Show full text]
  • Nonlinear Control Systems
    1. Introduction to Nonlinear Systems Nonlinear Control Systems Ant´onioPedro Aguiar [email protected] 1. Introduction to Nonlinear Systems IST-DEEC PhD Course http://users.isr.ist.utl.pt/%7Epedro/NCS2012/ 2011/2012 1 1. Introduction to Nonlinear Systems Objective The main goal of this course is to provide to the students a solid background in analysis and design of nonlinear control systems Why analysis? (and not only simulation) • Every day computers are becoming more and more powerful to simulate complex systems • Simulation combined with good intuition can provide useful insight into system's behavior Nevertheless • It is not feasible to rely only on simulations when trying to obtain guarantees of stability and performance of nonlinear systems, since crucial cases may be missed • Analysis tools provide the means to obtain formal mathematical proofs (certificates) about the system's behavior • results may be surprising, i.e, something we had not thought to simulate. 2 1. Introduction to Nonlinear Systems Why study nonlinear systems? Nonlinear versus linear systems • Huge body of work in analysis and control of linear systems • most models currently available are linear (but most real systems are nonlinear...) However • dynamics of linear systems are not rich enough to describe many commonly observed phenomena 3 1. Introduction to Nonlinear Systems Examples of essentially nonlinear phenomena • Finite escape time, i.e, the state can go to infinity in finite time (while this is impossible to happen for linear systems) • Multiple isolated equilibria, while linear systems can only have one isolated equilibrium point, that is, one steady state operating point • Limit cycles (oscillation of fixed amplitude and frequency, irrespective of the initial state) • Subharmonic, harmonic or almost-periodic oscillations; • A stable linear system under a periodic input produces an output of the same frequency.
    [Show full text]
  • Application of Symmetry and Symmetry Analyses to Systems of First-Order Equations Arising from Mathematical Modelling in Epidemiology
    Proceedings of Institute of Mathematics of NAS of Ukraine 2004, Vol. 50, Part 1, 159–169 Application of Symmetry and Symmetry Analyses to Systems of First-Order Equations Arising from Mathematical Modelling in Epidemiology P.G.L. LEACH † and K. ANDRIOPOULOS ‡ † School of Mathematical and Statistical Sciences, University of Natal, Durban 4041, South Africa E-mail: [email protected] ‡ Department of Mathematics, National and Capodistrian University of Athens, Panepistimioupolis, Ilisia, 15771 Athens, Greece E-mail: [email protected] We examine the integrability, in terms of the Painlev´e singularity analysis and of the Lie symmetry analysis, of systems of nonlinear first-order ordinary differential equations that arise in the particular area of Mathematical Modelling known as Rational Epidemiology. These analyses are presented as being complementary to the standard analysis using the methods of Dynamical Systems. The importance to obtain complete understanding of evo- lution of epidemics – one need think only of the potential for devastation by HIV-AIDS in African countries or the more recent threat posed by SARS – demands that all possi- ble approaches of analysis be used. The concept of decomposed systems is introduced as illustrating some rather attractive mathematical properties of certain classes of systems of equations arising in Mathematical Modelling. Such systems allow the mathematician some opportunity to enjoy Mathematics even in the context of quite strict applications. 1 Introduction There are four standard approaches to the analysis of a system of nonlinear first-order ordi- nary differential equations of the type which arise frequently in Mathematical Modelling. The approaches comprise numerical computation, dynamical systems, singularity analysis and sym- metry analysis, all of which possess extensive literatures.
    [Show full text]
  • Nonlinear Control - an Overview
    1 NONLINEAR CONTROL - AN OVERVIEW Fernando Lobo Pereira, fl[email protected] Porto University, Portugal Nonlinear Control, 2008, FEUP References 1 M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall, Englewood Cli®s, NJ, 1978. 2 A. Isidori, Nonlinear Control Systems, Springer-Verlag, 199X. 3 E. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer-Verlag, 1998. 4 C. T. Chen, Introduction to Linear Systems Theory, Van Nostrand Reinhold Company, New York, NY, 1970. 5 C. A. Desoer, Notes for a Second Course on Linear Systems, Holt Rhinehart, Winston, 1970. 6 K. Ogata, State Space Analysis of Control Systems, Prentice-Hall, Englewood Cli®s, NJ, 1965. 7 J. M. Carvalho, Dynamical Systems and Automatic Control, Prentice-Hall, New York, NY, 1994. Fernando Lobo Pereira, fl[email protected] 1 Nonlinear Control, 2008, FEUP Introduction Problem description - system components, objectives and control issues. Example 1: telescope mirrors control PICTURE Most of real systems involve nonlinearities in one way or another. However, many concepts for linear systems play an important role since some of the techniques to deal with nonlinear systems are: ² Change of variable in phase space so that the resulting system is linear. ² Nonlinearities may be cancelled by picking up appropriate feedback control laws. ² Pervasive analogy ... Fernando Lobo Pereira, fl[email protected] 2 Nonlinear Control, 2008, FEUP Introduction Example 2: Pendulum Modeling PICTURE Dynamics (Newton's law for rotating objects): mθÄ(t) + mgsin(θ(t)) = u(t) State variables: θ; θ_ Control/Input variable: u (external applied torque) Let us assume m = 1; l = 1; g = 1. Fernando Lobo Pereira, fl[email protected] 3 Nonlinear Control, 2008, FEUP Introduction Control Design ½ (0; 0) stable equilibrium Stationary positions: (1) (¼; 0) unstable equilibrium.
    [Show full text]
  • Viewpointviewpoint Complexity in Biology
    viewpointviewpoint Complexity in biology Exceeding the limits of reductionism and determinism using complexity theory Fulvio Mazzocchi he ultimate aim of scientific research scientific knowledge has to provide an objec- due course, reductionism proved to be an is to understand the natural world. In tive representation of the external world. The extremely powerful analytical methodology Torder to achieve this goal, Western world’s apparent complexity can be resolved and it enabled scientists to analyse many science has relied on different cognitive by analysis and reducing phenomena to basic molecular and cellular processes. strategies, including simplification, both in their simplest components. “Once you have terms of analysis and explanation. As the done that, [the evolution of phenomena] Complex systems exist at British natural philosopher Sir Isaac Newton will turn out to be perfectly regular, revers- (1643–1727) put it, “Truth is ever to be ible and predictable, while the knowledge different levels of organization found in the simplicity, and not in the multi- you gained will merely be a reflection of that that range from the subatomic plicity and confusion of things.” In a way, pre-existing order” (Heylighen et al, 2007). realm to individual organisms to examples of simplification include using Ever since Newton formulated the first whole populations and beyond idealized models, such as a ‘perfect sphere laws of gravity, the conceptual model of the rolling down a smooth plane in a vacuum’; physical world had successfully described conducting experiments in a strictly con- the shape, movements and actions of the Nonetheless, biologists might be reaching trolled environment such as the laboratory; objects within it.
    [Show full text]