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Control (optimal control theory)
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<p>In <a href="/facts/Optimal_control_theory/9SmcQHjJ">optimal control theory</a>, a control is a variable chosen by the controller or <a href="/facts/Agent_(economics)/9dTPUnFk">agent</a> to manipulate <a href="/facts/State_variables/HNF1dCXu">state variables</a>, similar to an actual <a href="/facts/Control_valve/7cE7Jt09">control valve</a>. Unlike the state variable, it does not have a predetermined <a href="/facts/Equation_of_motion/25msr1vE">equation of motion</a>. The goal of optimal control theory is to find some <a href="/facts/Sequence/gV2S4uqp">sequence</a> of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a <a href="/facts/Loss_function/xv5ozuhl">loss function</a>). </p><p>A control given as a function of time only is referred to as an <i><a href="/facts/Open-loop_control/vjRIkFzd">open-loop control</a></i>. 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 <i><a href="/facts/Closed-loop_control/aIuERpn6">closed-loop control</a></i>. </p>