Optimal control: Difference between revisions

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'''Optimal control theory''' is a mathematical field that is concerned with control policies that can be deduced using [[optimization (mathematics)|optimization]] algorithms.

The control whichthat minimizes a certain [[cost functional]] is called the '''optimal control'''. It can be derived using [[Pontryagin's minimum principle]], or by solving the [[Hamilton-Jacobi-Bellman equation]].

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A simple example should clarify the issue: consider a car traveling on a straight line through a hilly road. The question is, how should the driver press the accelerator pedal in order to ''minimize'' the total traveling time? Clearly in this example, the term control law refers specifically to the way in which the driver presses the accelerator and shifts the gears. The system is intended to be both the car and the hilly road, and the optimality criterion is the minimization of the total traveling time. The problem formulation usually also contains [[constraint]]s. For example the amount of available fuel might be limited, the accelerator pedal cannot be pushed through the floor of the car, etc.