Abstract
In deriving the maximum principle and the transversality conditions of the optimal control problems for distributed parameter systems, the vector measure is still a useful tool. The finite codimension of the target set Q is important to the maximum principle.
Projects supported by the Science Fund of the Chinese Academy of Sciences.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Balakrishnan, A.V.: Applied Functional Analysis, Springer-Verlag, 1979.
Berkovitz, L.D.: Optimal Control Theory (Applied Mathematical Science, Vol. 12), Springer-Verlag, New York, 1974.
Curtain, R.F., Pritchard, A.J.: Infinite Dimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences 8, Springer-Verlag, 1978.
Diestel, J., Uhl, J.J., Jr.: Vector Measure, Amer. Math. Soc., Providence, Rhode Island, 1977.
Gamkrelidze, R.V.: Principles of Optimal Control Theory, Translation editor L.D. Berkovitz, Plenum Press, New York and London, 1978.
Klee, V.: Separation and support properties of Convex Sets — A Survey, in "Control Theory and the Calculus of Variations", Edited by A.V. Balakrishnan, Acad. Press, New York, 1969.
Lee, E.B., Markus, L.: Foundations of Optimal Control Theory, Wiley, New York, 1967, p. 251.
Li Xunjing and Yao Yunlong: On Optimal Control for Distributed Parameter Systems, Proc. of 8th IFAC World Congress, Kyoto J., 1981
Li Xunjing and Yao Yunglong: On Applications of Vector Measure to the Optimal Control Theory for Distributed Parameter Systems, Chin. Ann. of Math. 3(5), 1982, 655–662.
Pontryagin, L.S., Boltyanskii V.G., Gamkrelidze, R.V. and Mishchenko, E.F.: The Mathematical Theory of Optimal Processes, J. Wiley, New York, 1962.
Uhl, J.J.: The Range of a Vector-valued Measure, Proc. Amer. Math. Soc. 23 (1969), 158–163.
Yao Yunlong: Maximum Principle of Semi-linear Distributed Systems, Proc. of 3rd IFAC Symposium on Control of Distriubed Parameter Systems, Toulouse, F., 1982.
Yao Yunlong: Vector Measure and Maximum Principle of Distributed Parameter Systems, SCIENTIA SINICA(A), Vol. XXVI, No. 1, 1983, 102–112.
Yao Yunlong: Some Results of Unbounded Perturbation, Fudan J., (Natural Science) Vol. 22, No. 1, 1983, pp. 48–57.
Yao Yunlong: Optimal Control for a Class of Elliptic Equations, Control Theory and Applications, Vol. 1, No. 3, July 1984, pp. 17–23.
Yao Yunlong: The Regulator Problem of Pointwise Control for Parabolic Systems, Proc. of 9th World Congress of IFAC, Budapest, H., 1984.
Yao Yunlong: A Structure on the Unbounded Control, Chin. Ann. of Math., Vol. 5 Ser. A, No. 3, 1984, pp. 261–272.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Li, X., Yao, Y. (1985). Maximum principle of distributed parameter systems with time lags. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005665
Download citation
DOI: https://doi.org/10.1007/BFb0005665
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15872-1
Online ISBN: 978-3-540-39661-1
eBook Packages: Springer Book Archive