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

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Models for Research and Understanding: Exploring Dynamic Systems, Unconventional Approaches, and ApplicationsSuurem pilt
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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 simulation Includes sections of questions and answers, helpful in didactic work Proposes new methodology in addition to examining conventional approaches Offers some cognitive, more abstract models to give a wider insight on model building





















The books 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.
1 Concept of Model
1(24)
1.1 Introduction: General Remarks
1(2)
1.2 The System
3(1)
1.3 Mathematical Models
3(7)
1.3.1 Kinds of Mathematical Models
5(1)
1.3.2 Models of Economic Growth
6(1)
1.3.3 Models in Public Health and Epidemics
7(2)
1.3.4 Graphical Representations of Continuous Models
9(1)
1.3.5 Computational Tractability
10(1)
1.4 Discrete-Event Models
10(2)
1.4.1 Petri Nets
11(1)
1.4.2 Discrete-Event Specification Formalism (DEVS)
11(1)
1.5 Experimental Frames and Model Validity
12(5)
1.5.1 Two Capacitors Circuit
15(1)
1.5.2 Birth-and-death Process
16(1)
1.6 Model Credibility
17(1)
1.7 Uncertainty and Randomness
17(1)
1.8 Conclusion
18(1)
1.9 Questions and Answers
18(7)
References
21(4)
2 Continuous System Models
25(56)
2.1 Introduction
25(1)
2.2 Dynamic Systems
26(3)
2.2.1 General Classification
28(1)
2.3 Linearity
29(1)
2.4 Ordinary Differential Equations and Models of Systems with Concentrated Parameters
30(2)
2.5 Transfer Function
32(6)
2.5.1 Stability of Linear Models
34(1)
2.5.2 Routh--Hurwitz Stability Criterion
34(2)
2.5.3 Frequency Response
36(2)
2.6 Nyquist Plot and Stability Criterion
38(1)
2.7 Analog Computer Models
39(1)
2.8 Z-transform
40(5)
2.8.1 Matched Pole-zero
44(1)
2.9 Non-linear Models and Stability
45(6)
2.9.1 BIBO Stability
46(1)
2.9.2 Lyapunov Stability
46(1)
2.9.3 Asymptotic Stability
46(1)
2.9.4 Orbital Stability
47(4)
2.10 Stiff Equations
51(1)
2.11 Example: ODE Model of a Car Suspension
52(4)
2.12 Graphical Representations of Continuous Models
56(9)
2.12.1 Block Diagrams and Signal Flow Graphs
56(2)
2.12.2 Mason's Gain Formula
58(3)
2.12.3 Bond Graphs
61(2)
2.12.4 Example of Bond Graph
63(1)
2.12.5 The Causality and DYMOLA
64(1)
2.13 Models with Distributed Parameters, Partial Differential Equations
65(5)
2.13.1 PDE Solution Algorithms
65(3)
2.13.2 Finite Element Model
68(1)
2.13.3 Example: Jet Takeoff Vibrations
69(1)
2.14 Conclusion
70(1)
2.15 Questions and Answers
70(11)
References
78(3)
3 Differential Inclusions, Uncertainty, and Functional Sensitivity
81(26)
3.1 Introduction, Some Definitions
81(2)
3.2 Differential Inclusions
83(1)
3.3 Reachable Set
83(2)
3.4 Differential Inclusions and Control Systems
85(2)
3.4.1 Uncertainty Treatment
86(1)
3.5 Functional Sensitivity
87(1)
3.6 Differential Inclusion Solver
88(7)
3.6.1 Example: A Second-Order Model
93(2)
3.7 Discrete Differential Inclusions
95(6)
3.7.1 Reachable Set, Optimal Trajectory
96(2)
3.7.2 Example 1
98(2)
3.7.3 Example 2
100(1)
3.8 Conclusion
101(1)
3.9 Questions and Answers
102(5)
References
103(4)
4 Functional Sensitivity Applications
107(34)
4.1 Introduction
107(1)
4.2 Functional Sensitivity
108(2)
4.2.1 Differential Inclusions
108(1)
4.2.2 Sensitivity Analysis
108(2)
4.3 Differential Inclusion Solver
110(1)
4.4 Example: The Lotka--Volterra Model
111(2)
4.5 A Mechanical System
113(2)
4.6 Functional Sensitivity of the V/f Speed Control of Induction Motor
115(6)
4.6.1 Comparison with the Classical Sensitivity Analysis
119(2)
4.7 PID Anti-Windup Control
121(6)
4.8 Vehicle Horizontal Movement
127(3)
4.9 Marketing Sensibility and Reachable Sets
130(7)
4.9.1 The Model
131(3)
4.9.2 Experiment 1
134(1)
4.9.3 Experiment 2
135(2)
4.10 Conclusion
137(1)
4.11 Questions and Answers
138(3)
References
138(3)
5 Attainable Sets in Flight Control
141(10)
5.1 Introduction
141(1)
5.2 Control and Reachable Sets
142(5)
5.2.1 Airplane Dynamics
142(2)
5.2.2 Attainable Sets
144(3)
5.3 Conclusion
147(1)
5.4 Questions and Answers
147(4)
References
148(3)
6 Modeling, Simulation, and Optimization
151(20)
6.1 Introduction
151(2)
6.2 Landing on the Moon
153(3)
6.3 Iterative Algorithm
156(1)
6.4 Market Optimization
157(6)
6.5 Computer Implementation: Simulation and Optimization
163(4)
6.6 Conclusion
167(1)
6.7 Questions and Answers
167(4)
References
169(2)
7 Discrete Event Models
171(18)
7.1 Introduction
171(2)
7.2 The Event Queue
173(1)
7.3 Agent-Based Models
174(3)
7.3.1 People Agents
176(1)
7.4 Discrete Event Specification Formalism (DEVS)
177(2)
7.4.1 A Remark on Ambiguity
177(1)
7.4.2 DEVS
178(1)
7.5 Petri Nets
179(1)
7.6 Distributed Simulation Models
180(2)
7.7 Conclusion
182(1)
7.8 Questions and Answers
182(7)
References
185(4)
8 Self-Organization, Organization Dynamics, and Agent-Based Model
189(18)
8.1 Introduction
189(3)
8.2 The Model
192(5)
8.2.1 Interaction Rules
195(2)
8.3 BLUESSS Simulation Package
197(1)
8.4 Simulations
198(3)
8.5 Conclusion
201(2)
8.6 Questions and Answers
203(4)
References
204(3)
9 The Space of Models, Semi-Discrete Events with Fuzzy Logic
207(22)
9.1 Introduction
207(2)
9.1.1 Distance Between Models
208(1)
9.2 Strictly Discrete Event Model
209(2)
9.3 Finite-Time Event Model
211(7)
9.3.1 The Chicken Game
212(2)
9.3.2 Semi-Discrete Model Specification
214(3)
9.3.3 Model Coupling
217(1)
9.4 More Examples
218(6)
9.4.1 Example 1: One Server
218(3)
9.4.2 Example 2: Two Servers
221(2)
9.4.3 Example 3: A Battlefield
223(1)
9.5 Singularity of the Exact DES Models
224(2)
9.6 Conclusion
226(1)
9.7 Questions and Answers
226(3)
References
227(2)
10 Models and Categories
229(8)
10.1 Introduction: The Language of Categories
229(5)
10.1.1 Examples
230(3)
10.1.2 Simultaneous Events
233(1)
10.2 Conclusion
234(1)
10.3 Questions and Answers
234(3)
References
235(2)
11 Fuzzy Time Instants and Time Model
237(10)
11.1 Introduction
237(1)
11.2 The Fuzzy Time Instant
238(6)
11.2.1 Example
242(2)
11.3 Conclusion
244(3)
References
245(2)
12 Uncertain Future, Reversibility and the Fifth Dimension
247(32)
12.1 Introduction
247(1)
12.2 Uncertain Future
247(2)
12.3 Differential Inclusion Solver
249(2)
12.4 Solving the Ideal Predictor Problem. Feedback From the Future
251(7)
12.4.1 Example 1: A Linear Model
252(2)
12.4.2 Example 2: A Non-Linear Model
254(1)
12.4.3 Example 3: A Control System
254(4)
12.5 Reversibility
258(3)
12.5.1 Irreversibility of Differential Inclusions
259(2)
12.6 Encapsulated Universe and the Fifth Dimension
261(18)
12.6.1 General Remarks
262(1)
12.6.2 The Ball
263(1)
12.6.3 The Metric Structure
264(1)
12.6.4 Linear Vector Space Operators
265(2)
12.6.5 Local Ball and Local Observer
267(1)
12.6.6 Velocity Superposition
268(1)
12.6.7 Particle Movement and a Small Bang
269(2)
12.6.8 Adding the Time Dimension
271(1)
12.6.9 Uncertainty and Traveling Beyond the Infinity
272(3)
12.6.10 The Fifth Dimension
275(1)
12.6.11 Conclusion
276(1)
References
277(2)
Index 279
Stanislaw Raczynski received his master degree (1964) from the Academy of  Mining and Metallurgy (AGH, now called Technical University of Krakow) in Krakow Poland, Electrical Engineering Department, his PhD. (1969) and Habilitation degree (1977)  from the same Academy,  in the area of control theory and optimization methods.  In 1964 Dr. Raczynski joined the Institute for Automatics  and Industrial Electronics of the Academy of Mining and Metallurgy in Krakow. From 1971 through 1972, he was the head of the Computer  Center of the AGH.  Between 1973 and 1976 he worked as a researcher in  the International Research Group in Moscow, USSR (located in the Institute for Control Problems of the Academy of Sciences of the USSR).  The  research  area  was operations research and computer simulation.  In 1976  Dr. Raczynski became head of  the  Systems  Analysis Group  at  the Academy of Mining andMetallurgy  in  Krakow.   From 1980 through  1983  he participated in the activities of the European Workshop on Industrial  Computer Systems. Between 1983 and 1986 he was a visiting professor of the National University of Mexico.  In 1986 Dr. Raczynski joined the Panamericana University in Mexico City, Engineering Department.  His didactic activities include courses on control theory, electronics and computer simulation.





 





Between 1996 and 2000 and then between 2002 and 2004 Dr. Raczynski had been the International Director of The Society for Computer Simulation. In 2003-2004 is the international co-director of the McLeod Institute for Simulation Sciences (part of The Society  for  Computer  Simulation in San Diego, California). From 1996 up to now he is a member of the National System of Researchers of Mexico. Between 1994 and 2003 Dr. Raczynski was the director of the Mexican Center of the McLeod Institute of Simulation Sciences. He wrote two books on computer simulation and has more than 140 articles and papers published in professional journals and conference proceedings.
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