Time Optimal Control of Semilinear Control Systems Involving Time Delays

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

   Article  MATH  MathSciNet  Google Scholar 

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

   Article  MATH  MathSciNet  Google Scholar 

3. Jeong, J.M.: Retarded functional differential equations with \(L^1\)-valued controller. Funkc. Ekvacioj 36, 71–93 (1993)

   MATH  Google Scholar 

4. Yong, J., Pan, L.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 

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

   Article  MATH  MathSciNet  Google Scholar 

6. Mordukhovich, B.S., Wang, D., Wang, L.: Optimal control of delay-differential inclusions with functional endpoint constraints in infinite dimensions. Nonlinear Anal. 71, 2740–2749 (2009)

   Article  MathSciNet  Google Scholar 

7. Mordukhovich, B.S., Wang, D., Wang, L.: Optimization of delay-differential inclusions in infinite dimensions. Pac. J. Optim. 6, 353–374 (2010)

   MATH  MathSciNet  Google Scholar 

8. Micu, S., Roventa, I., Tucsnak, M.: Time optimal boundary controls for the heat equation. J. Funct. Anal. 263, 25–49 (2012)

   Article  MATH  MathSciNet  Google Scholar 

9. Krakowiak, A.: Time optimal control of retarded parabolic systems. IMA J. Math. Control Inf. 24, 357–369 (2007)

   Article  MATH  MathSciNet  Google Scholar 

10. Fattorini, H.O.: Time and norm optimal controls: a survey of recent results and open problems. Acta Math. Sci. Ser. B Engl. Ed. 31, 2203–2218 (2011)

    Article  MATH  MathSciNet  Google Scholar 

11. Tanabe, H.: Fundamental solutions for linear retarded functional differential equations in Banach space. Funkc. Ekvacioj 35, 239–252 (1992)

    MathSciNet  Google Scholar 

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

    Book  Google Scholar 

13. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

15. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. Amsterdam, North-Holland (1978)

    Google Scholar 

16. Aubin, J.P.: Un théorème de compacité. C. R. Acad. Sci. 256, 5042–5044 (1963)

    MATH  MathSciNet  Google Scholar 

Download references