Journal of Optimization Theory and Applications

, Volume 3, Issue 6, pp 385–391 | Cite as

Estimation of optimality for multidimensional control systems

  • A. W. J. Stoddart


Consider a class of functionsY, U on a multidimensional domainA, satisfying a differential equationY′=h(x, Y, U) and given restrictions on values. We seek good lower bounds for a multiple integral\(\int_A {f(x,Y,U)dx} \) over such a class. For givenY, U, such lower bounds allow one to estimate the closeness of the integral to its infimum.


Control System Lower Bound Good Lower Bound Multidimensional domainA Multidimensional Control 
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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  1. 1.
    Gould, S. H.,Variational Methods for Eigenvalue Problems, University of Toronto Press, Toronto, Canada, 1957.Google Scholar
  2. 2.
    Krotov, V. F.,Approximate Synthesis of Optimal Controls, Automation and Remote Control, Vol. 25, No. 11, 1964.Google Scholar
  3. 3.
    Rozenberg, G. S.,Analytical Estimation of the Degree of Optimality of Controlled Systems, Automation and Remote Control, Vol. 27, No. 10, 1966.Google Scholar
  4. 4.
    Krotov, V. F.,Methods for the Solution of Variational Problems Using Sufficient Conditions for an Absolute Minimum III, Automation and Remote Control, Vol. 25, No. 7, 1964.Google Scholar

Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • A. W. J. Stoddart
    • 1
  1. 1.Department of MathematicsWestern Michigan UniversityKalamazoo

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