Abstract
In this paper, we consider a convex optimal control problem involving a class of linear hyperbolic partial differential systems. A computational algorithm which generates minimizing sequences of controls is devised. The convergence properties of the algorithm are investigated.
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Suryanarayana, M. B.,Necessary Condition for Optimization Problems with Hyperbolic Partial Differential Equations, SIAM Journal on Control, Vol. 11, No. 1, 1973.
Cesari, L.,Optimization with Partial Differential Equations in Dieudonné-Rashevsky Form and Conjugate Problems, Archive for Rational Mechanics and Analysis, Vol. 33, pp. 339–357, 1969.
Suryanarayana, M. B.,Existence Theorems for Optimization Problems Concerning Linear, Hyperbolic Partial Differential Equations without Convexity Conditions, Journal of Optimization Theory and Applications, Vol. 19, No. 1, 1976.
Wu, Z. S., andTeo, K. L.,First-Order Strong Variation Algorithm for Optimal Control Problem Involving Hyperbolic Systems, Journal of Optimization Theory and Applications, Vol. 39, No. 4, 1983.
Barnes, E. R.,An Extension of Gilbert's Algorithm for Computing Optimal Controls, Journal of Optimization Theory and Applications, Vol. 7, No. 6, 1971.
Himmelberg, C. J., Jacobs, M. Q., andVan Vleck, F. S.,Measurable Multiplications, Selectors, and Filippov's Implicit Function Lemma, Journal of Mathematical Analysis and Applications, Vol. 25, pp. 276–284, 1969.
Cesari, L.,Existence Theorems for Multidimensional Problems of Optimal Control, Differential Equations and Dynamical Systems, Edited by J. K. Hale and J. P. LaSalle, Academic Press, New York, New York, 1967.
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Communicated by L. Cesari
This work was done during the period when Z. S. Wu was an Honorary Visiting Fellow in the School of Mathematics at the University of New South Wales, Australia.
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Wu, Z.S., Teo, K.L. A convex optimal control problem involving a class of linear hyperbolic systems. J Optim Theory Appl 39, 541–560 (1983). https://doi.org/10.1007/BF00933757
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DOI: https://doi.org/10.1007/BF00933757