Formulation of the Control Problem

  • Leonard D. Berkovitz
Part of the Applied Mathematical Sciences book series (AMS, volume 12)


In this chapter we first point out the common mathematical structure of the examples in the previous chapter. This permits a somewhat imprecise preliminary formulation of the mathematical problem of optimal control. It should, however, motivate the precise and more general formulation of the mathematical problem of optimal control which is given in Section 3. In Section 4 we discuss various equivalent formulations of the problem, and in Section 5 we show how some other control problems can be cast in the form given in Section 3. We conclude this chapter with a discussion of the relationship between problems in the calculus of variations and control problems. Sections 4 to 6 inclusive can be omitted at a first reading and can be read as the need arises.


Control Problem Admissible Control Admissible Pair Control Constraint Isoperimetric Problem 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Leonard D. Berkovitz
    • 1
  1. 1.Division of Mathematical SciencesPurdue UniversityWest LafayetteUSA

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