In
optimal control theory
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
, a control is a variable chosen by the controller or
agent
Agent may refer to:
Espionage, investigation, and law
*, spies or intelligence officers
* Law of agency, laws involving a person authorized to act on behalf of another
** Agent of record, a person with a contractual agreement with an insuranc ...
to manipulate
state variables
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...
, similar to an actual
control valve
A control valve is a valve used to control fluid flow by varying the size of the flow passage as directed by a signal from a controller. This enables the direct control of flow rate and the consequential control of process quantities such as pressu ...
. Unlike the state variable, it does not have a predetermined
equation of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
. The goal of optimal control theory is to find some
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a
loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost ...
).
A control given as a function of time only is referred to as an ''open-loop control''. In contrast, a control that gives optimal solution during some remainder period as a function of the state variable at the beginning of the period is called a ''closed-loop control''.
See also
*
Control loop
A control loop is the fundamental building block of industrial control systems. It consists of all the physical components and control functions necessary to automatically adjust the value of a measured process variable (PV) to equal the value of ...
References
Control loop theory
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