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Annali di Matematica Pura ed Applicata

, Volume 109, Issue 1, pp 165–176 | Cite as

Extremal points and optimal control theory

  • J. E. Rubio
Article

Summary

An optimal control problem is considered in a setting akin to that of the theory. of generalized curves. Rather than minimizing a functional depending on pairs of trajectories and controls subject to some constraints, a functional defined on a set of Radon measures is considered; the set of measures is determined by the constraints. An approximation scheme is developed, so that the solution of the optimal control problems can be effected by solving a sequence of nonlinear programming problems. Several existence theorems for this kind of generalized control problems are then proved; the most interesting is the one concerning problems in which the set of allowable controls is unbounded.

Keywords

Control Problem Programming Problem Control Theory Optimal Control Problem Extremal Point 
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.

References

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    L. Cesari,Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints - II:Existence theorems for weak solutions, Trans. Amer. Math. Soc.,124, no. 3 (1966).Google Scholar

Copyright information

© Fondazione Annali di Matematica Para ed Applicata 1975

Authors and Affiliations

  • J. E. Rubio
    • 1
  1. 1.Leeds

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