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Control Theory

Computation, Optimization and Control

Control theory is a field of control engineering and applied mathematics that studies how to influence the behavior of dynamical systems so that they reach and hold a desired state. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Central Question
Given a dynamical system and a way to influence it through some input, does feedback based on the system's own output keep that system's behavior bounded and stable, or does it drive the system away from the state a designer intends. 1
Key Debate
How old the mathematical treatment of control really is against how recent the field's formal identity is. Control theory dates from the nineteenth century, when James Clerk Maxwell first gave a theoretical account of how mechanical governors operate, but the field did not crystallize as its own branch of applied mathematics, with a general stability criterion such as bounded-input bounded-output stability, until long after engineers had already been building feedback devices by intuition alone. 1
Classification
Pure or Applied
Applied Mathematics 1
Connections

Associated With

Aleksandr Lyapunov, Mathematicians

Lyapunov's own entity-description: "his 1892 doctoral thesis The General Problem of the Stability of Motion, which founded what is now called Lyapunov stability theory, central to the modern study of dynamical systems and control theory." He carried no branch edge of any kind before this write.

Source MacTutor History of Mathematics Archive
Sources
1. Control Theory (Wikipedia)
Wikipedia
  • Lead section, pure or applied classification
    Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems.
  • Stability
    A linear system is called bounded-input bounded-output (BIBO) stable if its output will stay bounded for any bounded input.
  • Lead paragraph
    Control theory dates from the 19th century, when the theoretical basis for the operation of governors was first described by James Clerk Maxwell.
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