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Applications of Control Theory in Ecology - Proceedings of the Symposium on Optimal Control Theory held at the State University of New York, Syracuse, New York, August 10-16, 1986 (Paperback, Softcover reprint of the original 1st ed. 1987)
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Applications of Control Theory in Ecology - Proceedings of the Symposium on Optimal Control Theory held at the State University of New York, Syracuse, New York, August 10-16, 1986 (Paperback, Softcover reprint of the original 1st ed. 1987)
Series: Lecture Notes in Biomathematics, 73
Expected to ship within 10 - 15 working days
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Control theory can be roughly classified as deterministic or
stochastic. Each of these can further be subdivided into game
theory and optimal control theory. The central problem of control
theory is the so called constrained maximization (which- with
slight modifications--is equivalent to minimization). One can then
say, heuristically, that the major problem of control theory is to
find the maximum of some performance criterion (or criteria), given
a set of constraints. The starting point is, of course, a
mathematical representation of the performance criterion (or
criteria)- sometimes called the objective functional--along with
the constraints. When the objective functional is single valued
(Le., when there is only one objective to be maximized), then one
is dealing with optimal control theory. When more than one
objective is involved, and the objectives are generally
incompatible, then one is dealing with game theory. The first paper
deals with stochastic optimal control, using the dynamic
programming approach. The next two papers deal with deterministic
optimal control, and the final two deal with applications of game
theory to ecological problems. In his contribution, Dr. Marc Mangel
applies the dynamic proQramming approach, as modified by his recent
work--with Dr. Colin Clark, from the University of British Columbia
(Mangel and Clark 1987}*--to modelling the "behavioral decisions"
of insects. The objective functional is a measure of fitness.
Readers interested in detailed development of the subject matter
may consult Mangel (1985). My contributions deal with two
applications of optimal control theory."
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