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Successive approximation method in optimum distributed-parameter systems

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Abstract

The problem of controlling a linear distributed-parameter system with a nonquadratic error measure is discussed. The calculus of variations approach is used to derive an algorithm based on the first variation for theN-dimensional linear diffusion process. The procedure for determining whether the resulting solution is optimum is discussed. Extension of the algorithm for other linear distributed-parameter systems is indicated.

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References

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    Kelley, H. J.,Method of Gradients, Optimization Techniques, Edited by G. Leitmann, Academic Press, New York, 1962.

  2. 2.

    Bryson, A. E., andDenham, W.,A Steepest-Descent Method for Solving Optimum Programming Problems, Journal of Applied Mechanics, Vol. 29, No. 2, 1962.

  3. 3.

    Kim, M., andGajwani, S. H.,A Variational Approach to Optimum Distributed Parameter Systems, IEEE Transactions on Automatic Control, Vol. AC-13, 1968.

  4. 4.

    Kim, M.,Optimality Conditions for Distributed Parameter Systems (to appear).

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Additional information

This research was supported in part by the National Science Foundation, Grant No. GK-304.

Communicated by Y. C. Ho

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Kim, M. Successive approximation method in optimum distributed-parameter systems. J Optim Theory Appl 4, 40–43 (1969). https://doi.org/10.1007/BF00928715

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Keywords

  • Error Measure
  • Approximation Method
  • Diffusion Process
  • Variation Approach
  • Successive Approximation