Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. T. Banks, Representations for solutions of linear functional differential equations, J. Differential Equations 5(1969), 399–409.
H. T. Banks, Variational problems involving functional differential equations, SIAM J. Control 7(1969), 1–17.
H. T. Banks, A maximum principle for optimal control problems with functional differential systems, Bull. Amer. Math. Soc. 75(1969), 158–161.
R. Bellman and K. L. Cooke, "Differential Difference Equations", Academic Press, New York, 1963.
C. Castaing, Sur les multi-applications measurables, Rev. Francaise Informat. Recherche Operationelle 1(1967), 91–126.
D. H. Chyung and E. B. Lee, Optimal systems with time delays, Proc. 3rd IFAC Conf. London, 1966.
A. Halanay, "Differential Equations", Academic Press, New York, 1966.
A. Halanay, frLe "principe du maximum" pour les systemes optimaux lineaires a retardement, C. R. Acad. Sci. Paris 254(1962), 2277–2279.
H. Halkin, A generalization of LaSalle's "Bang-Bang" principle, SIAM J. Control 2(1964), 199–202.
C. J. Himmelberg, M. Q. Jacobs, and F. S. Van Vleck, Measurable multifunctions, selectors, and Filippov's implicit functions lemma, J. Math. Anal. Appl. 25(1969), 276–284.
M. Q. Jacobs, Measurable multivalued mappings and Lusin's theorem, Trans. Amer. Math. Soc. 134(1968), 471–481.
K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13(1965), 397–403.
E. B. Lee, Variational problems for systems having delay in the control action, IEEE Trans. AC-13(1968), 697–699.
E. B. Lee, Geometric theory of linear controlled systems, to appear.
N. Levinson Minimax, Liapunov and "Bang-Bang", J. Differential Equations 2(1966), 218–241.
L. W. Neustadt, The existence of optimal controls in the absence of convexity conditions, J. Math. Anal. Appl. 7(1963), 110–117.
C. Olech, Extremal solutions to a control system, J. Differential Equations 2(1966), 74–101.
M. N. Oguztöreli, "Time-Lag Control Systems", Academic Press, New York, 1966.
E. Pinney, "Ordinary Difference-Differential Equations", Univ. Calif. Press, 1958.
V. Volterra, "Theory of Functionals", Blackie, London, 1930.
A. M. Zverkin, G. A. Kemenskii, S. B. Norkin, and L. E. El'sgol'ts, Differential equations with a perturbed argument I and II, Russian Math. Surveys 17(1962), 61–146 and Trudy Sem. Teor. Differencial. Uravnenii s Otklon. Argumentom 2(1963), 3–49.
Editor information
Rights and permissions
Copyright information
© 1970 Springer-Verlag
About this paper
Cite this paper
Banks, H.T., Jacobs, M.Q. (1970). Optimal control and linear functional differential equations. In: Yorke, J.A. (eds) Seminar on Differential Equations and Dynamical Systems, II. Lecture Notes in Mathematics, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059914
Download citation
DOI: https://doi.org/10.1007/BFb0059914
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-04933-3
Online ISBN: 978-3-540-36306-4
eBook Packages: Springer Book Archive