Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

OPTIMAL PROBLEM OF REGULAR COST FUNCTION FOR RETARDED SYSTEM

  • Jong-Yeoul Park (Department of Mathematics Pusan National University Pusan 609-739, Korea) ;
  • Jin-Mun Jeong (Division of MAthematical Sciences Pukyong National University Pusan 608-737, Korea) ;
  • Young-Chel Kwun (Department of Mathematics Dong-A University Pusan 604-714, Korea)
  • Published : 1998.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

Keywords

References

  1. J. Integral Eq. and Appl. v.2 Stabilizability of intgrodifferential parabolic equations G. Da Prato;L. Lunardi
  2. J. Math. Anal. Appl. v.102 $L^2$-regularity for parabolic partial integrodifferential equations with depay in the highest-order derivative G. Di Blasio;K. Kunisch;E. Sinestrari
  3. SIAM J. Control. Optim. v.17 The riccati integral equations for optimal control problems on Hilbert spaces J.S. Gibson
  4. Osaka J. Math. v.28 Stabilizability of retarded functional differential equation in Hilbert space J.M. Jeong
  5. Funkcial. Ekvac. v.36 retarded functional differential equations with $L^1$-valued controller J.M. Jeong
  6. Optimal Control of Systems Governed by Partial Differential Equations J.L. Lions
  7. Isaka J. Math. v.25 Structural properties of functional differential equations in Banach spaces S. Nakgiri
  8. J. Math. Anal. Appl. v.120 Optimal control of linear retarded systems in Banach space S. Nakagiri
  9. Japan J. Appl. Math. v.2 Observsbility, controllability, and feedback stabilizability for evolution equations Ι T. Suzuki;M. Yamamoto
  10. Equations of Evolution H. Tanabe
  11. Funkcial. Ekvac. v.35 Fundamental solution of differential equation with time delay in Banach space H. Tanabe