 Once initial conditions formula_5 and controls formula_6 are specified, a solution to the differential equations, called a "trajectory" formula_7, can be found.The problem of optimal control is to choose formula_6 (from some compact and convex set formula_9) so that formula_10 maximizes or minimizes a certain objective function between an initial time formula_11 and a terminal time formula_12 (where formula_13 may be infinity).Specifically, the goal is to optimize a performance index formula_14 at each point in time,
subject to the above equations of motion of the state variables.