Optimal Control Theory and Renewable Resource Management

Abstract

This is a brief report on some applications of optimal control theory to problems in biological resource exploitation. In some respects the models employed are similar to well-known models in economics (growth theory, pollution control, etc.), as described in the lectures of Professor Dobell at this seminar. What makes bio-economic models particularly interesting, though, is the interplay between two dynamic systems, the biological on the one hand and the economic on the other. The economic system expends resources (labour and capital) in order to achieve a harvest, which, via the operations of a market, in turn provides an input to the economic system. Harvesting also affects the dynamics of the biological system, frequently in complex ways that are only vaguely understood, and hence, since the effectiveness of the harvesting program depends upon the state of the biological system, present harvesting always has an effect on future economic returns. Analyses based on equilibrium concepts such as “maximum sustained yield” are obviously incapable of taking these facts into account.