Branches of Mathematics
Control Theory
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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.
Facts
Central QuestionGiven 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 DebateHow 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 Cross-Tradition Connections
Sources
1. Control Theory (Wikipedia)
WikipediaStabilityQuote, Stability
A linear system is called bounded-input bounded-output (BIBO) stable if its output will stay bounded for any bounded input.
1. Control Theory (Wikipedia)
WikipediaLead paragraphQuote, 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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