Abstract
We study dual or complementary variational principles for functionals with deviating argument and discontinuous extremals. Local conditions for the existence of a pair of dual extremum principles are given. Results are then applied to the control problem involving linear neutral differential-difference equations.
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El'sgol'c, L. E.,Qualitative Methods of Mathematical Analysis, Translations of Mathematical Monographs, Vol. 12, American Mathematical Society, Providence, Rhode Island, 1964.
Hughes, D. K.,Variational and Optimal Control Problems with Delayed Argument, Journal of Optimization Theory and Applications, Vol. 2, pp. 1–14, 1968.
Sabbagh, L. D.,Variational Problems with Lags, Journal of Optimization Theory and Applications, Vol. 3, pp. 34–51, 1969.
Halanay, A.,Variational Problems with Delayed Argument, Delay and Functional Differential Equations, Theory and Applications, Edited by K. Schmitt, Academic Press, New York, New York, 1973.
Kamenskii, G. A.,Variational and Boundary-Value Problems with Deviating Argument, Differential Equations, Vol. 6, pp. 1026–1032, 1970.
Kamenskii, G. A.,On Extrema of Functionals with Deviating Arguments, Soviet Mathematics, Vol. 16, pp. 1380–1383, 1975.
Noble, B.,Complementary Variational Principles for Boundary Value Problems, I: Basic Principles with an Application to Ordinary Differential Equations, University of Wisconsin, Mathematics Research Center, Report No. 473, 1964.
Arthurs, A. M.,Complementary Variational Principles, Clarendon Press, Oxford, England, 1970.
Chan, W. L.,Dual Variational Principles with Delayed Argument, International Journal of Control, Vol. 20, pp. 1015–1019, 1974.
Chan, W. L.,Variational Dualities in the Linear Regulator and Estimation Problems with and without Time Delay, Journal of the Institute of Mathematics and Its Applications, Vol. 18, pp. 237–247, 1976.
Aggarwal, J. K., andEller, D. H.,Optimal Control of Neutral Systems, International Journal of Control, Vol. 14, pp. 309–319, 1971.
Conner, M. A.,A Gradient Method for Neutral Systems, Automatica, Vol. 9, pp. 639–641, 1973.
Datko, R.,Neutral Autonomous Functional Equations with Quadratic Cost, SIAM Journal on Control, Vol. 12, pp. 70–82, 1974.
Palm, W. J., andSchmitendorf, W. E.,Conjugate Points Conditions for Variational Problems with Delayed Argument, Journal of Optimization Theory and Applications, Vol. 14, pp. 599–612, 1974.
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Communicated by D. F. Lawden
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Chan, W.L., Tai, C.H. Dual variational principles with deviating argument and discontinuous extremals. J Optim Theory Appl 23, 593–605 (1977). https://doi.org/10.1007/BF00933299
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DOI: https://doi.org/10.1007/BF00933299