Reachable Sets of Dynamic Systems

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 TheSociety 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.

"The most important object…is the reachable set, which is understood as the union of graphs of all trajectories of the differential inclusion. Another essential concept developed by the author is functional sensitivity which is defined by using concepts of the calculus of variations... The principal feature of this monograph… is its constructive approach…recommended [for] students, researchers and engineers who are interested in control theory and differential inclusions as well as in the problems of computer simulation in these fields." --Valeri Obukhovskii, MathSciNet"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

• 1. Differential inclusions 2. Differential inclusion solver 3. Market optimization and uncertainty 4. Uncertainty in stock markets5. Flight maneuver reachable sets6. Vessel dynamics and reachable sets7. Mechanical systems: earthquakes and car suspensions8. PID control: functional sensitivity9. Speed control of an induction motor10. Uncertainty in public health: epidemics11. Uncertain future: a trip