Dynamics is what characterizes virtually all phenomenae we face
in the real world, and processes that proceed in practically all
kinds of inanimate and animate systems, notably social systems. For
our purposes dynamics is viewed as time evolution of some
characteristic features of the phenomenae or processes under
consideration. It is obvious that in virtually all non-trivial
problems dynamics can not be neglected, and should be taken into
account in the analyses to, first, get insight into the problem
consider, and second, to be able to obtain meaningful results.
A convenient tool to deal with dynamics and its related
evolution over time is to use the concept of a dynamic system
which, for the purposes of this volume can be characterized by the
input (control), state and output spaces, and a state transition
equation. Then, starting from an initial state, we can find a
sequence of consecutive states (outputs) under consecutive inputs
(controls). That is, we obtain a trajectory. The state transition
equation may be given in various forms, exemplified by differential
and difference equations, linear or nonlinear, deterministic or
stochastic, or even fuzzy (imprecisely specified), fully or
partially known, etc. These features can give rise to various
problems the analysts may encounter like numerical difficulties,
instability, strange forms of behavior (e.g. chaotic), etc.
This volume is concerned with some modern tools and techniques
which can be useful for the modeling of dynamics. We focus our
attention on two important areas which play a key role nowadays,
namely automation and robotics, and biological systems. We also add
some new applications which can greatly benefit from the
availability of effective and efficient tools for modeling
dynamics, exemplified by some applications in security systems.
General
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