An extension of the calculus of variations for dynamic systems with one independent variable, usually time, in which control (input) variables are determined to maximize (or minimize) some measure of the performance (output) of a system while satisfying specified constraints. The theory may be divided into two parts: optimal programming, where the control variables are determined as functions of time for a specified initial state of the system, and optimal feedback control, where the control variables are determined as functions of the current state of the system.