What is Optimal Control Theory

An extension of the calculus of variations, is a mathematical optimization method for deriving control policies. Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A control problem includes a cost functional that is a function of state and control variables. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. The optimal control can be derived using Pontryagin's maximum principle (a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's Principle), or by solving the Hamilton-Jacobi-Bellman equation (a sufficient condition).

Freshness Management in the Retail Business

Hisashi Kurata (University of Tsukuba, Japan) and Seong-Hyun Nam (University of North Dakota, USA)