Models for Research and Understanding: Exploring Dynamic Systems, Unconventional Approaches, and Applications

Description

This introductory textbook/reference addresses the fundamental and mostly applied kinds of models. The focus is on models of dynamic systems that move and change over time. However, the work also proposes new methods of uncertainty treatment, offering supporting examples. Topics and features: Chapters suitable for textbook use in teaching modeling and simulationIncludes sections of questions and answers, helpful in didactic workProposes new methodology in addition to examining conventional approachesOffers some cognitive, more abstract models to give a wider insight on model building The book’s readership may consist of researchers working on multidisciplinary problems, as well educators and students. It may be used while teaching computer simulation, applied mathematics, system analysis and system dynamics. Preface Acknowledgements Contents 1 Concept of Model 1.1 Introduction: General Remarks 1.2 The System 1.3 Mathematical Models 1.3.1 Kinds of Mathematical Models 1.3.2 Models of Economic Growth 1.3.3 Models in Public Health and Epidemics 1.3.4 Graphical Representations of Continuous Models 1.3.5 Computational Tractability 1.4 Discrete-Event Models 1.4.1 Petri Nets 1.4.2 Discrete-Event Specification Formalism (DEVS) 1.5 Experimental Frames and Model Validity 1.5.1 Two Capacitors Circuit 1.5.2 Birth-and-death Process 1.6 Model Credibility 1.7 Uncertainty and Randomness 1.8 Conclusion 1.9 Questions and Answers References 2 Continuous System Models 2.1 Introduction 2.2 Dynamic Systems 2.2.1 General Classification 2.3 Linearity 2.4 Ordinary Differential Equations and Models of Systems … 2.5 Transfer Function 2.5.1 Stability of Linear Models 2.5.2 Routh–Hurwitz Stability Criterion 2.5.3 Frequency Response 2.6 Nyquist Plot and Stability Criterion 2.7 Analog Computer Models 2.8 Z-transform 2.8.1 Matched Pole-zero 2.9 Non-linear Models and Stability 2.9.1 BIBO Stability 2.9.2 Lyapunov Stability 2.9.3 Asymptotic Stability 2.9.4 Orbital Stability 2.10 Stiff Equations 2.11 Example: ODE Model of a Car Suspension 2.12 Graphical Representations of Continuous Models 2.12.1 Block Diagrams and Signal Flow Graphs 2.12.2 Mason's Gain Formula 2.12.3 Bond Graphs 2.12.4 Example of Bond Graph 2.12.5 The Causality and DYMOLA 2.13 Models with Distributed Parameters, Partial Differential Equations 2.13.1 PDE Solution Algorithms 2.13.2 Finite Element Model 2.13.3 Example: Jet Takeoff Vibrations 2.14 Conclusion 2.15 Questions and Answers References 3 Differential Inclusions, Uncertainty, and Functional Sensitivity 3.1 Introduction, Some Definitions 3.2 Differential Inclusions 3.3 Reachable Set 3.4 Differential Inclusions and Control Systems 3.4.1 Uncertainty Treatment 3.5 Functional Sensitivity 3.6 Differential Inclusion Solver 3.6.1 Example: A Second-Order Model 3.7 Discrete Differential Inclusions 3.7.1 Reachable Set, Optimal Trajectory 3.7.2 Example 1 3.7.3 Example 2 3.8 Conclusion 3.9 Questions and Answers References 4 Functional Sensitivity Applications 4.1 Introduction 4.2 Functional Sensitivity 4.2.1 Differential Inclusions 4.2.2 Sensitivity Analysis 4.3 Differential Inclusion Solver 4.4 Example: The Lotka–Volterra Model 4.5 A Mechanical System 4.6 Functional Sensitivity of the V/f Speed Control of Induction Motor 4.6.1 Comparison with the Classical Sensitivity Analysis 4.7 PID Anti-Windup Control 4.8 Vehicle Horizontal Movement 4.9 Marketing Sensibility and Reachable Sets 4.9.1 The Model 4.9.2 Experiment 1 4.9.3 Experiment 2 4.10 Conclusion 4.11 Questions and Answers References 5 Attainable Sets in Flight Control 5.1 Introduction 5.2 Control and Reachable Sets 5.2.1 Airplane Dynamics 5.2.2 Attainable Sets 5.3 Conclusion 5.4 Questions and Answers References 6 Modeling, Simulation, and Optimization 6.1 Introduction 6.2 Landing on the Moon 6.3 Iterative Algorithm 6.4 Market Optimization 6.5 Computer Implementation: Simulation and Optimization 6.6 Conclusion 6.7 Questions and Answers References 7 Discrete Event Models 7.1 Introduction 7.2 The Event Queue 7.3 Agent-Based Models 7.3.1 People Agents 7.4 Discrete Event Specification Formalism (DEVS) 7.4.1 A Remark on Ambiguity 7.4.2 DEVS 7.5 Petri Nets 7.6 Distributed Simulation Models 7.7 Conclusion 7.8 Questions and Answers References 8 Self-Organization, Organization Dynamics, and Agent-Based Model 8.1 Introduction 8.2 The Model 8.2.1 Interaction Rules 8.3 BLUESSS Simulation Package 8.4 Simulations 8.5 Conclusion 8.6 Questions and Answers References 9 The Space of Models, Semi-Discrete Events with Fuzzy Logic 9.1 Introduction 9.1.1 Distance Between Models 9.2 Strictly Discrete Event Model 9.3 Finite-Time Event Model 9.3.1 The Chicken Game 9.3.2 Semi-Discrete Model Specification 9.3.3 Model Coupling 9.4 More Examples 9.4.1 Example 1: One Server 9.4.2 Example 2: Two Servers 9.4.3 Example 3: A Battlefield 9.5 Singularity of the Exact DES Models 9.6 Conclusion 9.7 Questions and Answers References 10 Models and Categories 10.1 Introduction: The Language of Categories 10.1.1 Examples 10.1.2 Simultaneous Events 10.2 Conclusion 10.3 Questions and Answers References 11 Fuzzy Time Instants and Time Model 11.1 Introduction 11.2 The Fuzzy Time Instant 11.2.1 Example 11.3 Conclusion References 12 Uncertain Future, Reversibility and the Fifth Dimension 12.1 Introduction 12.2 Uncertain Future 12.3 Differential Inclusion Solver 12.4 Solving the Ideal Predictor Problem. Feedback From the Future 12.4.1 Example 1: A Linear Model 12.4.2 Example 2: A Non-Linear Model 12.4.3 Example 3: A Control System 12.5 Reversibility 12.5.1 Irreversibility of Differential Inclusions 12.6 Encapsulated Universe and the Fifth Dimension 12.6.1 General Remarks 12.6.2 The Ball 12.6.3 The Metric Structure 12.6.4 Linear Vector Space Operators 12.6.5 Local Ball and Local Observer 12.6.6 Velocity Superposition 12.6.7 Particle Movement and a Small Bang 12.6.8 Adding the Time Dimension 12.6.9 Uncertainty and Traveling Beyond the Infinity 12.6.10 The Fifth Dimension 12.6.11 Conclusion References Appendix Index Index