Optimal control theory. A set of mathematical techniques and theorems concerned with finding optimal time-paths of particular systems. The state of the system at any point in time is completely described by the

Optimal growth theory numerical values of a set of variables called state variables. The values of these variables, and so the state of the system, change over time according to some dynamic relationships which must be specified mathematically. There is a second set of variables, called the control variables, whose values at each point in time are to be chosen by the decision-taker and which then determine the time-paths of the state variables. The decision-taker will have a preference ordering over alternative time-paths of the system, and this must also be specified mathematically. Optimal control theory then studies the problem of choosing those time-paths of the control variables out of the set of paths which are feasible, which leads to the preferred time-path of the entire system.

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