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First-order strong variation algorithm for optimal control problems involving hyperbolic systems

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Abstract

This paper considers an optimal control problem involving linear, hyperbolic partial differential equations. A first-order strong variational technique is used to obtain an algorithm for solving the optimal control problem iteratively. It is shown that the accumulation points of the sequence of controls generated by the algorithm (if they exist) satisfy a necessary condition for optimality.

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References

  1. Suryanarayana, M. B.,Necessary Conditions for Optimization Problems with Hyperbolic Partial Differential Equations, SIAM Journal on Control, Vol. 11, pp. 130–147, 1973.

    Google Scholar 

  2. Suryanarayana, M. B.,Existence Theorem for Optimization Problems Concerning Linear, Hyperbolic Partial Differential Equations without Convexity Conditions, Journal of Optimization Theory and Applications, Vol. 19, pp. 47–62, 1976.

    Google Scholar 

  3. Suryanarayana, M. B.,Optimization Problems with Hyperbolic Partial Differential Equations, University of Michigan, Doctoral Thesís, 1969.

  4. Ahmed, N. U., andTeo, K.,Optimal Control of Distributed-Parameter Systems, Elsevier North-Holland, Amsterdam, Holland, 1981.

    Google Scholar 

  5. Reid, D. W.,On the Computational Methods for Optimal Control of Distributed Parameter Systems, University of New South Wales, Doctoral Thesis, 1980.

  6. Cesari, L.,Optimization with Partial Differential Equations in Dieudonné-Rashevshy Form and Conjugate Problems, Archive for Rational Mechanics and Analysis, Vol. 33, pp. 339–357, 1969.

    Google Scholar 

  7. Ladyzhenskaja, O. A., Solonikov, V. A., andUral'Ceva, N. N.,Linear and Quasilinear Equations of Parabolic Type (English Translation), American Mathematical Society, Providence, Rhode Island, 1968.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, China

    Z. S. Wu (Lecturer)

  2. Department of Applied Mathematics, University of New South Wales, Kensington, New South Wales, Australia

    K. L. Teo (Senior Lecturer)

Authors
  1. Z. S. Wu
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  2. K. L. Teo
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Additional information

Communicated by L. Cesari

The authors wish to thank Professor L. Cesari for his most valuable comments and suggestions. This work was done during the period when Z. S. Wu was an Honorary Visiting Fellow in the School of Mathematics at the University of New South Wales, Australia.

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Wu, Z.S., Teo, K.L. First-order strong variation algorithm for optimal control problems involving hyperbolic systems. J Optim Theory Appl 39, 561–587 (1983). https://doi.org/10.1007/BF00933758

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  • DOI: https://doi.org/10.1007/BF00933758

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