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Proofs of the Necessary Condition for Control Problems and Related Topics

  • Lamberto Cesari
Part of the Applications of Mathematics book series (SMAP, volume 17)

Abstract

Let A denote the constraint set, a closed subset of the tx-space, with t in R, and the space variable x = (x1,…, x n ) in R n . Let U(t),the control set, be a subset of the u-space R m , u= (u1, …u m )the control variable. Let M = [(t,x,u)|(t,x)∈A, uU(t)] be a closed subset of R1+n+m, and let f = (f1,…,fn) be a continuous vector function from M into Rn. Let the boundary set B be a closed set of points (t1,x1,t2,x2) in R2n+2, x1 = (x 1 1 ,…x 1 n ), x2 = (x 2 1 ,…x 2 n ). Let g be a continuous function from B into R.

Keywords

Control Problem Closed Subset Convex Cone Lebesgue Point Supporting Hyperplane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Lamberto Cesari
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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