Abstract
It is proposed to find an athlete's optimal strategy for running a race of arbitrary lengthX. A mathematical model is set up of the dependence of his physical state at any time upon the history of his efforts up to that time. An explicit optimal effort function is then obtained which minimizes the time taken to complete the race and therefore represents the athlete's optimal strategy.
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References
Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
Young, L. C.,Lectures on the Calculus of Variations and Optimal Control Theory, W. B. Saunders Company, Philadelphia, 1969.
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Communicated by D. F. Lawden
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Lawden, G.H. Optimal use of a self-regenerating controller that decays with use. J Optim Theory Appl 11, 121–131 (1973). https://doi.org/10.1007/BF00935877
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DOI: https://doi.org/10.1007/BF00935877