Journal of Optimization Theory and Applications

, Volume 14, Issue 5, pp 521–528 | Cite as

A lower closure theorem for abstract control problems withLp-bounded controls

  • L. D. Berkovitz
Contributed Papers


A lower closure theorem for an abstract control problem is proved. The functional isJ(ϕ,u)=∝ G f0(t, (Mϕ)(t),u(t))dt and the state equations areNϕ(t)=f(t, (Mϕ)(t),u(t)). It is shown that, if {(ϕ k ,uk)} is a sequence of admissible controlsuk and corre-sponding trajectories ϕ k such that lim infJ k ,uk)<+∞ and such that ϕ k → ϕ weakly,Mϕ k Mϕ strongly,Nϕ k Nϕ weakly, and {uk} is bounded in someLp norm, then there is a controlu such that (ϕ,u) is admissible and lim infJ k ,uk)≧J(ϕ,u).

Key Words

Lower closure theorems generalized control theory control theory calculus of variations 


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Copyright information

© Plenum Publishing Corporation 1974

Authors and Affiliations

  • L. D. Berkovitz
    • 1
  1. 1.Department of MathematicsPurdue UniversityLafayette

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