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Optimal initial functions of retarded control systems. (English) Zbl 0881.49018
Summary: This paper deals with the optimization problem of initial functions and optimality conditions for retarded functional equations for the given cost functions. Under ensuring the regularity of the solution of the retarded system we proceed to necessary optimality condition of the optimal solution for the cost function in the set of admissible controls that is closed and convex.
MSC:
49K25 Optimal control problems with equations with ret.arguments (nec.) (MSC2000)
49N60 Regularity of solutions in optimal control
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References:
[1] G. Da Prato, L. Lunardi: Stabilizability of integrodifferential parabolic equations. J. Integral Equations 2 (1990), 2, 281-304. · Zbl 0697.45007 · doi:10.1216/JIE-1990-2-2-281
[2] G. Di Blasio K. Kunisch, E. Sinestrari: \(L^2\)-regularity for parabolic partial integrodifferential equations with delay in the highest-order derivative. J. Math. Anal. Appl. 102 (1984), 38-57. · Zbl 0538.45007 · doi:10.1016/0022-247X(84)90200-2
[3] J. S. Gibson: The Riccati integral equations for optimal control problems on Hilbert spaces. SIAM J. Control Optim. 17 (1979), 4, 537-565. · Zbl 0411.93014 · doi:10.1137/0317039
[4] J. M. Jeong: Stabilizability of retarded functional differential equation in Hilbert space. Osaka J. Math. 28 (1991), 347-365. · Zbl 0755.34081
[5] J. M. Jeong: Retarded functional differential equations with \(L^1\)-valued controller. Funkcial. Ekvac. 36 (1993), 71-93. · Zbl 0791.35140
[6] J. L. Lions: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin–New York 1971. · Zbl 0203.09001
[7] S. Nakagiri: Structural properties of functional differential equations in Banach spaces. Osaka J. Math. 25 (1988), 353-398. · Zbl 0713.34069
[8] S. Nakagiri: Optimal control of linear retarded systems in Banach space. J. Math. Anal. Appl. 120 (1986), 169-210. · Zbl 0603.49005 · doi:10.1016/0022-247X(86)90210-6
[9] T. Suzuki, M. Yamamoto: Observability, controllability, and feedback stabilizability for evolution equations I. Japan J. Appl. Math. 2 (1985), 211-228. · Zbl 0593.93028 · doi:10.1007/BF03167045
[10] H. Tanabe: Equations of Evolution. Pitman, London 1979. · Zbl 0417.35003
[11] H. Tanabe: Fundamental solution of differential equation with time delay in Banach space. Funkcial. Ekvac. 35 (1992), 149-177 · Zbl 0771.34060
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