Abstract
Nearly forty years ago — on the publication of Pontryagin’s treatise — control theory was born as a separate mathematical discipline. Much has been accomplished since then, new results have indeed been forthcoming. The theory of necessary conditions has been developed successfully; existence theory is comprehensive and sophisticated; the control of systems described by partial differential equations has been exhaustively studied, and there have been many advances in optimization theory. Indeed, the subject seems to be in a period of consolidation, following an era of change and progress.
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References
Rubio J.E, “Weak global controllability of nonlinear systems”, Journal of Optimization Theory and its Applications, vol.39, pp. 251–259, Feb.1983.
Rubio J.E., “Control and Optimization: the Linear Treatment of Nonlinear Problems”, to be published in 1985 by Manchester University Press.
Young L.C., “Calculus of Variations and Optimal Control Theory”. Philadelphia; W.B. Saunders, 1969.
Schaefer H.H., “Topological Vector Spaces”. New York: Macmillan, 1966.
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© 1985 Springer-Verlag Berlin Heidelberg
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Rubio, J.E. (1985). Nonlinear Optimal Control Problems as Infinite-Dimensional Linear Programming Problems. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_13
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DOI: https://doi.org/10.1007/978-3-642-46564-2_13
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