Abstract
Two computational procedures for solving a class of bottleneck problems with state delay are presented. The first one uses a direct computation scheme for the solution of the continuous-time problem, while the second one is obtained by discretizing the continuous-time problem using piecewise constant controls on small intervals. Examples show that these two approaches agree.
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References
Bellman, R. E., Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
Grinold, R., Symmetric Duality for Continuous Linear Programs, SIAM Journal on Applied Mathematics, Vol. 18, pp. 84–97, 1970.
Murray, J. M., Some Existence and Regularity Results for Dual Linear Control Problems, Journal of Mathematical Analysis and Application, Vol. 112, pp. 190–209, 1985.
Rockafellar, R. T., Duality in Optimal Control, Mathematical Control Theory, Edited by W. A. Coppel, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 680, pp. 219–257, 1978.
Rockafellar, R. T., Linear-Quadratic Programming and Optimal Control, SIAM Journal on Control and Optimization, Vol. 25, pp. 781–814, 1987.
Mirică, S., Optimal Feedback Control for a Class of Bottleneck Problems, Journal of Mathematical Analysis and Applications, Vol. 112, pp. 221–235, 1985.
Teo, K. L., Wong, K. H., and Clements, D. J., Optimal Control Computation for Linear Time-Lag Systems with Linear Terminal Constraints, Journal of Optimization Theory and Applications, Vol. 44, pp. 509–526, 1984.
Halanay, A., Differential Equations, Academic Press, New York, New York, 1966.
Gale, D., The Theory of Linear Economic Models, McGraw-Hill, New York, New York, 1960.
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Bătătorescu, A. Optimal Solution of a Bottleneck Problem with State Delay. Journal of Optimization Theory and Applications 97, 339–356 (1998). https://doi.org/10.1023/A:1022678717478
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DOI: https://doi.org/10.1023/A:1022678717478