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Estimation of optimality for multidimensional control systems

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Abstract

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.

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References

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    Gould, S. H.,Variational Methods for Eigenvalue Problems, University of Toronto Press, Toronto, Canada, 1957.

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    Krotov, V. F.,Approximate Synthesis of Optimal Controls, Automation and Remote Control, Vol. 25, No. 11, 1964.

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    Rozenberg, G. S.,Analytical Estimation of the Degree of Optimality of Controlled Systems, Automation and Remote Control, Vol. 27, No. 10, 1966.

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    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.

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Additional information

This research was performed under a Faculty Research Fellowship at Western Michigan University, Kalamazoo, Michigan.

Communicated by M. R. Hestenes

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Stoddart, A.W.J. Estimation of optimality for multidimensional control systems. J Optim Theory Appl 3, 385–391 (1969). https://doi.org/10.1007/BF00929354

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Keywords

  • Control System
  • Lower Bound
  • Good Lower Bound
  • Multidimensional domainA
  • Multidimensional Control