Literature Cited
A. G. Butkovskii, “Control of distributed parameter systems,” Avtomat. Telemekh., No. 11, 16–65 (1979).
P. K. C. Wang, “Theory of stability and control for distributed parameter systems,” Int. J. Control,7, No. 2 (1968).
K. A. Lur'e, Optimal Control in Problems of Mathematical Physics [in Russian], Nauka, Moscow (1975).
J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations [Russian translation], Mir, Moscow (1972).
A. G. Butkovskii, Optimal Control Theory of Distributed Parameter Systems [in Russian], Nauka, Moscow (1965).
V. I. Plotnikov, “Necessary and sufficient conditions for optimality, and conditions for the uniqueness of optimizing functions for control systems of a general form,” Izv. Akad. Nauk SSSR, Ser. Mat.,36, 652–670 (1972).
A. I. Egorov, “Necessary conditions for optimality for distributed parameter systems,” Mat. Sb.,69, No. 3, 371–421 (1966).
L. Cezari, “Optimization with partial differential equations in Dieudonné-Rashevsky form, and conjugate problems,” Arch. Rat. Mech. Anal.,33, No. 5, 339–357 (1969).
M. I. Novozhenov and V. I. Plotnikov, “A generalized rule for Lagrange multipliers for distributed systems with phase constraints,” Differents. Uravn.,18, No. 4, 584–592 (1982).
A. I. Moskalenko, “A class of optimal control problems,” Zh. Vychisl. Mat. Mat. Fiz.,9, No. 1, 68–95 (1969).
A. S. Matveev and V. A. Popov, “Optimal control of distributed parameter systems in a domain with a moving boundary, and in the presence of phase constraints,” Vestn. Leningr. Gos. Univ., Ser. Mat., Mekh., Astron., Moscow (1981). Dep. at VINITI 19.02.81, No. 3015-81.
V. A. Yakubovich, “On the abstract theory of optimal control,” Sib. Mat. Zh.,19, No. 2, 436–460 (1978).
I. K. Gogodze, “Necessary conditions for optimality in elliptic control problems with integral constraints,” Soobshch. Akad. Nauk Gruz. SSR,81, No. 1, 17–20.
Yu. A. Kuznetsov, “Necessary conditions for optimality in the control of systems described by equations of elliptic type,” Sib. Mat. Zh.,20, No. 3, 586–596 (1979).
I. Ekeland, “Sur le contrôle optimal des systèmes gouvernés par des équations elliptiques,” J. Functional Anal.,9, No. 1, 1–62 (1972).
T. Zolezzi, “Necessary conditions for optimal control of elliptic and parabolic problems,” SIAM J. Control,10, No. 4, 594–607 (1972).
A. V. Dmitruk, A. A. Milyutin, and N. P. Osmolovskii, “Lyusternik's theorem and the theory of extrema,” Usp. Mat. Nauk,35, No. 6, 11 (1980).
L. Schwartz, Analysis [Russian translation], Vol. 1, Mir, Moscow (1972).
H. Schaefer, Topological Vector Spaces, MacMillan, New York (1966).
J. L. Kelley, General Topology, Van Nostrand, New York (1955).
V. G. Boltyanskii, “Homotopy theory of continuous maps and vector fields,” Tr. Mat. Inst. Steklova, Akad. Nauk SSSR,47, 233–297 (1955).
O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions, and Embedding Theorems [in Russian], Nauka, Moscow (1976).
V. A. Solonnikov, “On general boundary value problems for systems elliptic in the sense of Douglis-Nirenberg,” Tr. Mat. Inst. Steklova, Akad. Nauk SSSR,92, 233–297 (1966).
V. A. Solonnikov, “Lp-estimates of solutions of elliptic and parabolic systems,” Tr. Mat. Inst. Steklova, Akad. Nauk SSSR,120, 137–160 (1967).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 1, pp. 94–107, January–February, 1988.
Rights and permissions
About this article
Cite this article
Matveev, A.S. Abstract theory of the optimal control of distributed parameter systems. Sib Math J 29, 73–83 (1988). https://doi.org/10.1007/BF00975018
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00975018