Stanislaw Raczynski

Differential Inclusions in Modeling and Simulation Stanislaw Raczynski

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.