In optimal control theory, a control is a variable chosen by the controller or agent to manipulate state variables, similar to an actual control valve. Unlike the state variable, it does not have a predetermined equation of motion.[1] The goal of optimal control theory is to find some sequence of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a loss function).
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.[2]