Log in :: RSS/Atom Feeds
Kodai Mathematical Journal

Existence theory of optimal controls for distributed parameter systems

Jiong Min Yong

Source: Kodai Math. J. Volume 15, Number 2 (1992), 193-220.

Primary Subjects: 49J27
Secondary Subjects: 34G20, 34H05

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.kmj/1138039597
Mathematical Reviews number (MathSciNet): MR1185418
Zentralblatt MATH identifier: 0770.49005
Digital Object Identifier: doi:10.2996/kmj/1138039597

References

[1] N. U. AHMED, Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space, J. Optim. Theory &Appl., 50 (1986), 213-237.
Mathematical Reviews (MathSciNet): MR857234
Zentralblatt MATH: 0577.49025
[2] N. U. AHMED AND K. L. TEO, Optimal Control of Distributed Parameter Systems, North Holland, NewYork, 1981
Mathematical Reviews (MathSciNet): MR624064
Zentralblatt MATH: 0472.49001
[3] J. M. BALL, Strong continuous semigroups, weak solutions and the variation o constants formula, Proc. Amer. Soc, 63 (1972), 372-373.
[4] V. BARBU, Optimal Control of Variational Inequalities, Pitman, London, 1984
Mathematical Reviews (MathSciNet): MR742624
Zentralblatt MATH: 0574.49005
[5] L. D. BERKOVITZ, Optimal Control Theory, Springer-Verlag, New York, 1974
Mathematical Reviews (MathSciNet): MR372707
Zentralblatt MATH: 0295.49001
[6] L. D. BERKOVITZ, Existence and lower closure theorems for abstract contro problems, SIAM J. Control, 12 (1974), 27-42.
Mathematical Reviews (MathSciNet): MR341254
Zentralblatt MATH: 0243.93012
[7] J. F. BONNANS AND D. TIBA, Pontryagin principle in the control of semilinea elliptic variational inequalities, Appl. Math. Optim., 23 (1991), 299-312.
Mathematical Reviews (MathSciNet): MR1095664
Zentralblatt MATH: 0728.49003
[8] N. BOURBAKI, General Topology, Addison-Wesley Reading, 1966
[9] H. BREZIS, Problemes unilatereaux, J. Math. Pure Appl., 51 (1972), 1-168
Mathematical Reviews (MathSciNet): MR428137
Zentralblatt MATH: 0237.35001
[10] L. CESARI, Existence theorems for weak and usual Lagrange problems wit unilateral constraints I, II, Trans. Amer. Math. Soc, 124 (1966), 369-427.
Mathematical Reviews (MathSciNet): MR203542
Zentralblatt MATH: 0145.12501
[11] L. CESARI, Existence theorems for abstract multidimensional control problems, J. Optim. Theory & Appl., 6 (1970), pp. 210-236
Mathematical Reviews (MathSciNet): MR271806
Zentralblatt MATH: 0188.48602
[12] L. CESARI, Geometric and analytic views in existence theorems for optima control in Banach spaces, I, II, III, J. Optim. Theory & Appl., 14 (1974), 505-520, 15 (1975), 467-497, 19 (1976), 185-214.
Zentralblatt MATH: 0272.49002
[13] L. CESARI, Existence of solutions and existence of optimal solutions, Mathe matical Theories of Optimization, J. P. Cecconi and T. Zolezzi eds., Lecture Notes in Math., Vol. 979, Sprmger-Verlag, Berlin, 1983, 88-107.
Mathematical Reviews (MathSciNet): MR713806
Zentralblatt MATH: 0509.49003
[14] L. CESARI, Optimization Theory and Applications, Problems with Ordinary Dif ferential Equations, Springer-Verlag, New York, 1983.
Mathematical Reviews (MathSciNet): MR688142
Zentralblatt MATH: 0506.49001
[15] R. F. CURTAIN AND A. J. PRITCHARD, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control and Information Scieces, Vol.8, Springer-Aerlag, Ne York, 1981.
Mathematical Reviews (MathSciNet): MR516812
Zentralblatt MATH: 0389.93001
[16] C. J. HIMMELBERG, M. Q. JACOBS AND F. S. VANVLECK, Measurable multifunc tions, selectors and Filippov's implicit functions lemma, J. Math. Anal. Appl., 25 (1969), 276-284.
Mathematical Reviews (MathSciNet): MR235089
Zentralblatt MATH: 0179.08303
[17] S. H. Hou, Existence theorems of optimal control problems in Banch spaces, Nonlinear Anal., 7 (1983), 239-257
Mathematical Reviews (MathSciNet): MR693442
Zentralblatt MATH: 0509.49004
[18] S. NABABAN AND K. L. TEO, On the existence of optimal controls of the firs boundary value problem for parabolic partial delay-differential equations m divergence form, J. Math. Soc. Japan, 32 (1980), 343-362.
Mathematical Reviews (MathSciNet): MR567424
[19] N. S. PAPAGEORGIOU, Existence of optimal controls for nonlinear systems i Banach spaces, J. Optim. Theory & Appl., 53 (1987), 451-459.
Mathematical Reviews (MathSciNet): MR891099
Zentralblatt MATH: 0596.49006
[20] N. S. PAPAGEORGIOU, Properties of the relaxed trajectories of evolution equation and optimal controls, SIAM J. Control & Optim. 27 (1989), 267-288.
Mathematical Reviews (MathSciNet): MR984828
Zentralblatt MATH: 0678.49002
[21] N. S. PAPAGEORGIOU, Existence of optimal controls for nonlinear distribute parameter systems, Funkcialaj Ekvacioj, 32 (1989), 429-437.
Mathematical Reviews (MathSciNet): MR1040170
Zentralblatt MATH: 0702.49006
[22] A. PAZY, Semigroups of Linear Operators and Applications to Partial Differentia Equations, Springer-Verlag, New York, 1983.
Mathematical Reviews (MathSciNet): MR710486
Zentralblatt MATH: 0516.47023
[23] R. TEMAM, Navier-Stokes Equations: Theory and Numerical Analysis, 3rdedi tion, North-Holland, Amsterdam, 1984.
Mathematical Reviews (MathSciNet): MR769654
Zentralblatt MATH: 0568.35002
[24] R. TORREJON AND J. YONG, A control problem for clamped extensible beams, Appl. Anal., 28 (1988), 163-180
Mathematical Reviews (MathSciNet): MR960003
Zentralblatt MATH: 0653.49016
[25] D. H. WAGNER, Survey of measurable selection theorems, SIAM J. Control Optim., 15 (1977), 859-903.
Mathematical Reviews (MathSciNet): MR486391
Zentralblatt MATH: 0407.28006
[26] J. WARGA, Optimal Control of Differential and Functional Equations, Academi Press, New York, 1972.
Mathematical Reviews (MathSciNet): MR372708
Zentralblatt MATH: 0253.49001
[27] J. YONG, Time optimal control for semilinear distributed parameter systems-existence theory and necessary conditions, Kodai Math. J., 14 (1991), 239-253.
Mathematical Reviews (MathSciNet): MR1123419
Zentralblatt MATH: 0764.49014
[28] E. ZEIDLER, Nonlinear Functional Analysis and Its Applications, I, Springer Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR816732
Zentralblatt MATH: 0583.47050

2010 © Tokyo Institute of Technology, Department of Mathematics