Differential Inclusions in Modeling and Simulation

Interdisciplinary Applications, Reachable Sets, Uncertainty Treatment for Educators and Researchers of Computer Modeling and Simulation

by Stanislaw Raczynski


View First 25 Pages: (free download)


The purpose of this book is to reach a circle of readers in the field of modeling and simulation, and similar. The examples and applications are multidisciplinary because of the multidisciplinary nature of modeling and simulation (MS). The book is not aimed for mathematicians, though some theoretical issues are also included. One of the aims of the book is to call into question a common paradigm that prevails among MS specialists telling that everything in the real world what is continuous in time, can be described by the ordinary or partial differential equations (ODEs, PDEs). My point is that this is not exactly true. So, we should look for a wider set of modeling tools. Differential inclusions (DIs) are used as an generalization of the ODE models.

An important topic of the book that appears in nearly all examples is the treatment of the uncertainty in dynamic models. The uncertainty is treated by a deterministic way. No statistical properties of uncertain parameters are used. The uncertain parameter is supposed to be constrained, which leads to a corresponding differential inclusion. The numerical results are obtained using the differential inclusion solver. Solutions of the differential inclusions (the reachable sets) are shown graphically. It should be noted that the presented images of the reachable sets have never been shown by other authors.

About the Author

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 and Metallurgy 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 70 articles and papers published in professional journals and conference proceedings.