On control and optimal control in biodynamic systems |
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Authors: | Robert Rosen |
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Institution: | (1) Department of Physiology and Biophysics, Dalhousie University, B3H 4H7 Halifax, Nova Scotia, Canada |
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Abstract: | In any control system for which the number of independent controls is smaller than the number of degrees of freedom to be
controlled, our choice of control in any state is restricted to a submanifold of smaller dimension than the tangent space.
This simple fact has a number of important consequences for questions of biological import; we consider its implications for
adaptation, for senescent phenomena and for the determination of tertiary structures of polypeptides through control of certain
average properties. We also formulate the Pontryagin Maximum Principle of Optimal control theory in such a way as to inquire
whether specific biodynamic systems can be regarded as optimal with respect to rate of accumulation of particular quantities
of the system. We find that if this is possible, the quantity in question must play the role of a clock. |
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