Introduction to the Mathematical Theory of Systems and Control

Control theory has two main roots: regulation and trajectory optimization. The first, regulation, is the more important and engineering oriented one. The second, trajectory optimization, is mathematics based. However, as we shall see, these roots have to a large extent merged in the second half of the twentieth century.
The problem of regulation is to design mechanisms that keep certain to-be- controlled variables at constant values against external disturbances that act on the plant that is being regulated, or changes in its properties. The system that is being controlled is usually referred to as the plant, a passepartout term that can mean a physical or a chemical system, for example. It could also be an economic or a biological system, but one would not use
the engineering term “plant” in that case.