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Optimal Control Problems for Semilinear Retarded Functional Differential Equations

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Abstract

This paper deals with the time optimal control problem for semilinear retarded functional differential equations by using the construction of the fundamental solution in the case where the principal operators are unbounded. We also present the maximum principle for controls which are described by the adjoint state corresponding to the linear equations without the condition of differentiability for the nonlinear term.

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References

  1. Yong, J., Pan, L.: Quasi-linear parabolic partial differential equations with delays in the highest order partial derivatives. J. Aust. Math. Soc. 54, 174–203 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Lions, J.L.: Contrôle optimal de systémes gouvernés par des équations aux dérivées partielles. Dunod, Gauthier-Villars, Paris (1968)

    MATH  Google Scholar 

  3. Nakagiri, S.: Optimal control of linear retarded systems in Banach spaces. J. Math. Anal. Appl. 120(1), 169–210 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Tanabe, H.: Equations of Evolution. Pitman, London (1979)

    MATH  Google Scholar 

  5. Papageorgiou, N.S.: Existence of optimal controls for nonlinear systems in Banach spaces. J. Optim. Theory Appl. 53(3), 1581–1600 (1987)

    Article  Google Scholar 

  6. Papageorgiou, N.S.: On the optimal control of strongly nonlinear evolution equations. J. Math. Anal. Appl. 164, 83–103 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Balakrishnan, A.V.: A computational approach to the maximum principle. J. Comput. Syst. Sci. 5, 163–191 (1971)

    Article  MATH  Google Scholar 

  8. Lions, J.L., Magenes, E.: Non-homogeneous Boundary Value Problems amd Applications I, II. Springer, Berlin (1972)

    Book  Google Scholar 

  9. Wang, P.K.C.: Optimal control of parabolic systems with boundary conditions involving time delay. SIAM J. Control 13, 274–293 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  10. Jeong, J.M., Kwun, Y.C., Park, J.Y.: Approximate controllability for semilinear retarded functional differential equations. J. Dyn. Control Syst. 5(3), 329–346 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Droniou, J., Raymond, J.P.: Optimal pointwise control of semilinear parabolic equations. Nonlinear Anal. 39, 135–156 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Di Blasio, G., Kunisch, K., Sinestrari, E.: \(L^2-\)regularity for parabolic partial integrodifferential equations with delay in the highest-order derivative. J. Math. Anal. Appl. 102, 38–57 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  13. Aubin, J.P.: Un thèoréme de compasité. C. R. Acad. Sci. 256, 5042–5044 (1963)

    MATH  MathSciNet  Google Scholar 

  14. Friedman, A.: Optimal control in Banach spaces. J. Math. Anal. Appl. 19, 35–55 (1967)

    Article  MATH  Google Scholar 

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Acknowledgments

This research was supported by Basic Science Research Program through the National research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014045161).

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    Jin-Mun Jeong & Hae-Jun Hwang

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  1. Jin-Mun Jeong
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  2. Hae-Jun Hwang
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Correspondence to Jin-Mun Jeong.

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Mark J. Balas.

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Jeong, JM., Hwang, HJ. Optimal Control Problems for Semilinear Retarded Functional Differential Equations. J Optim Theory Appl 167, 49–67 (2015). https://doi.org/10.1007/s10957-015-0726-8

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  • DOI: https://doi.org/10.1007/s10957-015-0726-8

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