Control theory

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Pontryagin maximum principle

A result in control theory. DefineThen in order for a control and a trajectory to be optimal, it is necessary that there exist nonzero absolutely continuous vector function corresponding to the functions and such that 1. The function attains its maximum at the point almost everywhere in the interval ,2. At the terminal time , the relations and are satisfied.

Little's law

Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the average time that an item spends in the system. Algebraically, this can expressed aswhere denotes the average number of items in the queuing system, is the average number of items arriving per unit time, and is the average waiting time for an item within the system.Due to its use of general language and its natural conditions with practically no extraneous assumptions, Little's law can be used to asymptotically describe conditions across a vast array of scenarios. For example, Little's law suggests that the average number of students attending a two-year college which averages 6,000 first-year student admissions per year is simply ...

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