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."

This vol ume contains the proceedings of the second U. S. -Austral ia workshop on Renewable Resource Management held at the East-West Center, Honolulu, Hawaii, December 9-12, 1985. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Science and Technology (Austral ia) under the U. S. -Austral ia Cooperative Science Program. The objective of the workshop was to focus on problems associated with the management of renewable resource systems. A particular emphasis was given to methods for handling uncertain elements whieh are present in any real system. Toward this end, the partiei pants were chosen so that the collective expertise included mathematical modeling, dynamical control/game theory, ecology, and practical management of real systems. Each participant was invited to give an informal presentation in his field of expertise as related to the overall theme. The formal papers (contained in this vo 1 ume) were written after the workshop so that the authors coul d util ize the workshop experience in relating their own work to others. To further encourage this exchange, each paper contained in this volume was reviewed by two other participants who then wrote formal comments. These comments (with author's reply in some cases) are attached to the end of each paper.