Mathematical Systems
Theory
Mathematical systems theory
is concerned with problems related to dynamic phenomena in interaction
with their environment.
These problems include:
• Modeling. Obtaining a
mathematical model that
reflects the main features. A mathematical model may be represented by
difference or differential equations, but also by inequalities,
algebraic equations, and logical constraints.
• Analysis and simulation of the
mathematical model.
• Prediction and estimation.
Identification of the
system behavior based on noisy and incomplete measurements.
• Control. By choosing inputs
or, more general, by
imposing additional constraints on some of the variables, the system
may be influenced so as to obtain certain desired behavior. Feedback is
an important example of control.
As the complexity and importance of our many industrial structures and
manufacturing systems grow, so does the guiding hand of Systems and
Control. This active research area is an important discipline in many
fields, involving such specialists as engineers, physicists,
mathematicians and designers.
The world of systems and control guides more of our lives than most of
us realise. Areas as diverse as the manufacturing and semiconductor
industry, infrastructure management, transportation, communications and
logistics, energy delivery, the medical profession, and the family
household are increasingly dependent on it. And as the world becomes
more and more
automated and guided, its impacts will spread even further.