Reachable Sets of Dynamic Systems
Uncertainty, Sensitivity, and Complex Dynamics
- 1st Edition - April 21, 2023
- Latest edition
- Author: Stanislaw Raczynski
- Language: English
Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its in… Read more
World Book Day celebration
Where learning shapes lives
Up to 25% off trusted resources that support research, study, and discovery.
Description
Description
Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its interdisciplinary applications. The design of dynamic systems of any type is an important issue as is the influence of uncertainty in model parameters and model sensitivity. The possibility of calculating the reachable sets may be a powerful additional tool in such tasks. This book can help graduate students, researchers, and engineers working in the field of computer simulation and model building, in the calculation of reachable sets of dynamic models.
Key features
Key features
- Introduces methodologies and approaches to the modeling and simulation of dynamic systems
- Presents uncertainty treatment and model sensitivity are described, and interdisciplinary examples
- Explores applications of differential inclusions in modeling and simulation
Readership
Readership
Table of contents
Table of contents
1. Differential inclusions
1.1. History and terminology
1.2. Some definitions
1.2.1. The reachable set
1.2.2. The tendor set
1.3. Differential inclusions and control systems
1.4. Uncertainty, differential games, and optimal control
1.5. Functional sensitivity
1.5.1. Functional sensitivity concept
1.5.2. Example: a non-linear model
1.6. Dualism and reachable sets
1.7. The inverse problem
1.8. The discrete version
1.8.1. Model 1: a linear rule
1.8.2. Model 2: non-linear model
1.8.3. Model 3: state variable restrictions
1.9. Conclusion
2. Differential inclusion solver
2.1. Main concepts
2.2. Solver algorithm
2.2.1. Multiprocessing
2.2.2. Example 1: non-linear second-order model
2.2.3. Example 2: model with two uncertain parameters
2.2.4. Example 3: mechanical fourth-order system
2.2.5. Example 4: DI in general form
2.2.6. Example 5: Lotka-Volterra equation
2.3. Conclusion
3. Market optimization and uncertainty
3.1. Some remarks on optimal control theory
3.2. Example: landing on the Moon
3.3. Simulation and optimization
3.4. The model
3.5. Computer implementation
3.6. Market models with uncertainty
3.6.1. Uncertainty problem
3.6.2. Differential inclusions
3.6.3. Differential inclusion solver
3.6.4. Application to a market model
3.6.5. Experiment 1: investment
3.6.6. Experiment 2: uncertain price elasticity
3.6.7. Experiment 3: model sensitivity
3.7. Conclusion
4. Uncertainty in stock markets
4.1. Stock market models and uncertainty
4.2. The model
4.3. Uncertainty in the stock market
4.4. Differential inclusion solver
4.5. Some results: uncertainty set
4.5.1. Experiment 1: uncertain erroneous information
4.5.2. Experiment 2: strong bandwagon effect
4.5.3. Experiment 3: smaller uncertainty range
4.6. Conclusion
5. Flight maneuver reachable sets
5.1. Differential inclusions and control systems
5.2. Application to aircraft maneuvers
5.3. Flight dynamics
5.4. Conclusion
6. Vessel dynamics and reachable sets
6.1. Differential inclusion and control systems
6.2. The model of movement
6.3. The reachable sets
6.4. Conclusions
7. Mechanical systems: earthquakes and car suspensions
7.1. Differential inclusions
7.2. The differential inclusion solver
7.3. An earthquake
7.4. Car suspension
7.5. Conclusion
8. PID control: functional sensitivity
8.1. System sensitivity
8.1.1. Functional sensitivity
8.2. Proportional, derivative, and integral control action
8.2.1. Windup in PID controllers
8.3. Differential inclusion solver
8.4. Calculating reachable sets
8.5. Conclusion
9. Speed control of an induction motor
9.1. Introduction: model sensitivity
9.2. V/f speed control of an induction motor
9.3. Functional sensitivity
9.3.1. Differential inclusions
9.3.2. Local and non-local sensitivity
9.3.3. Differential inclusion solver
9.4. Functional sensitivity of V/f control systems
9.4.1. Comparison with classical sensitivity analysis
9.5. Conclusion
10. Uncertainty in public health: epidemics
10.1. Epidemic dynamics
10.2. Modeling tool
10.3. Examples of reachable sets
10.3.1. The SIR model
10.3.2. The SIRS model
10.4. Conclusion
11. Uncertain future: a trip
11.1. Uncertain future
11.2. Differential inclusion solver
11.3. The ideal predictor: feedback from the future
11.3.1. Example 1: a linear model
11.3.2. Example 2: a non-linear model
11.3.3. Example 3: a control system
11.4. Conclusion
Review quotes
Review quotes
"In this book it is presented the so called tychastic approach to treatment of the uncertainty. This approach is suitable for situations, where probabilistic characteristics of the simulated objects data are hardly available, or they do not exist at all. Then, a more realistic information concerns the possible bounds for the values of the parameters. Such information may provide a rough assessment of the real system behavior, but in many cases, this may be the only way to obtain reasonable results. This way of treating uncertainty leads in a natural way to applications of differential inclusions that are generalizations of a ordinary differential equations and are used as a main modelling tool in the book."—Mikhail I. Krastanov, zbMATHOpen
Product details
Product details
- Edition: 1
- Latest edition
- Published: April 21, 2023
- Language: English
About the author
About the author
SR