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Optimization of systems governed by hyperbolic partial differential equation with equality and inequality constraints

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Abstract

An optimal control problem involving nonlinear hyperbolic partial differential equations, which includes restrictions on controls and equality and inequality constraints on the terminal states, is formulated. Using this problem, a framework for obtaining (first order) necessary conditions for control problems governed by partial differential equations with equality and inequality constraints is developed.

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References

  1. Ahmed N.U., Teo K.L.,Optimal Control of Distributed Parameter Systems, North Holland, New York, 1981.

    MATH  Google Scholar 

  2. Baum R., Cesari L.,On a Recent Proof of Pontryagin's Necessary Conditions, SIAM J. Control,10 1 (1972), pp. 56–72.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cesari L.,Optimization with Partial Differential Equations in Dieudonné-Rashevsky form and Conjugate Problems, Archiv. Rat. Mech. Anal.,33 5 (1968), pp. 339–357.

    MathSciNet  Google Scholar 

  4. Cesari L.,Optimization-Theory and Applications, Problems with Ordinary Differential Equations, Springer-Verlag, New York, Hildelberg, Berlin, 1983.

    MATH  Google Scholar 

  5. Dubovitsky A., Milutyn M.,Extremal Problems with Constraints, USSR Comp. Math. and Math. Physics,5 3 (1965).

  6. Egorov A.I.,Optimal Control Processes in Certain Parameter Systems, Automat. Remote Control,25 (1964), pp. 557–566.

    MATH  Google Scholar 

  7. Kazemi-Dehkordi M. A.,Optimal Control of Systems Governed by Partial Differential Equations and Integral Inequality Constraints, J. Nonlinear Analysis, Theory, Methods and Applications, to appear.

  8. Kazemi-Dehkordi M.A.,Necessary Conditions for Optimality of Singular Controls in Systems Governed by Partial Diferential Equations, J. Optimization, Theory and Applications,43 (1984) 629–638, 639–661.

    Article  MATH  MathSciNet  Google Scholar 

  9. Lasiecka I.,State Constrained Control Problems for Parabolic Systems: Regularity of Optimal Solutions, Appl. Math. Optim.6 (1980), pp. 1–29.

    Article  MATH  MathSciNet  Google Scholar 

  10. Mc Shane E. J.,Relaxed Controls and Variational Problems, SIAM J. Control,5 3 (1967), pp. 438–485.

    Article  MathSciNet  Google Scholar 

  11. Neustadt, L. W.,Optimization: A Theory of Necessary Conditions, Princeton University Press, Princeton, New Jersey, 1976.

    MATH  Google Scholar 

  12. Plotnikov V. I., Sumin V. I.,Optimization of Objects with Distributed Parameters Described by Goursat-Darboux Systems, USSR Comp. Math. and Math. Physics,12 1 (1972), pp. 67–77.

    MathSciNet  Google Scholar 

  13. Plotnikov V. I., Sumin V. I.,The Stability of Nonlinear Goursat-Darboux Systems, Diff. Equations,8 5 (1972), pp. 643–650.

    MATH  MathSciNet  Google Scholar 

  14. Srochko V. A.,Conditions for Optimality of a Class of Distributed Parameter Systems, Sib. Math. Journal,17 5 (1976), pp. 819–825.

    Article  Google Scholar 

  15. Suryanarayana M. B.,Necessary Conditions for Optimization Problems with Hyperbolic Partial Differential Equations, SIAM J. Control,2 1 (1973), pp. 130–137.

    Article  MathSciNet  Google Scholar 

  16. Suryanarayana M. B.,On Multidimentional Integral Equations of Voltra Type, Pacific J. Math.,41 (1972), pp. 808–828.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of North Caroline at Charlotte, 28223, Charlotte, N. C., U.S.A.

    M. A. Kazemi-Dehkordi

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  1. M. A. Kazemi-Dehkordi
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Kazemi-Dehkordi, M.A. Optimization of systems governed by hyperbolic partial differential equation with equality and inequality constraints. Rend. Circ. Mat. Palermo 34, 283–299 (1985). https://doi.org/10.1007/BF02850702

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  • DOI: https://doi.org/10.1007/BF02850702

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