Reachable Sets of Dynamic Systems
Uncertainty, Sensitivity, and Complex Dynamics
- 1st Edition - April 26, 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
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.
- 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
Graduate students, researchers, and professional engineers working in the fields of computer simulation and model building
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
- Edition: 1
- Latest edition
- Published: April 26, 2023
- Language: English
SR
Stanislaw Raczynski
Stanislaw Raczynski received his master’s, doctorate, and habilitation degrees in the area of control theory and optimization methods from the Academy of Mining and Metallurgy (AGH) in Krakow, Poland. He joined the Institute for Automatics and Industrial Electronics of AGH in 1964, and from 1971 through 1972, he headed its Computer Center. Between 1973 and 1976 he worked as a researcher in the International Research Group in Moscow, USSR, later becoming head of the Systems Analysis Group at the AGH. Dr. Raczynski joined Panamericana University in Mexico City in 1986. Between 1996 and 2000 and between 2002 and 2004, Dr. Raczynski was the International Director of The
Society for Computer Simulation. He wrote four books on computer simulation and has more than 140 articles and papers published in professional journals and conference proceedings.
Affiliations and expertise
Universidad Panamericana, MexicoRead Reachable Sets of Dynamic Systems on ScienceDirect