Control Problems and Sufficiency Considerations

  • John L. Troutman
Part of the Undergraduate Texts in Mathematics book series (UTM)


The discipline now identified as optimal control emerged during the decade 1940–1950, from the efforts by engineers to design electromechanical apparatus which was efficiently self-correcting, relative to some targeted objective. Such efficiency is clearly desirable in, say, the tracking of an aircraft near a busy airport or in the consumption of its fuel, and other economically desirable objectives suggest themselves. The underlying mathematical problems were attacked systematically in the next decade by Bellman [Be], by Hestenes [He], and by a Russian group under Pontjragin [Po]. Their results were quickly adapted to characterize optimal processes in other fields (including economics itself) and the feasibility of optimal control is now a standard consideration in contemporary design strategy.


Control Problem Optimal Control Problem State Equation Control Restriction Fixed Interval 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • John L. Troutman
    • 1
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

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