Parametric optimization with dynamic systems

摘要

Parametric optimization with dynamic systems may be viewed using two perspectives. If it is viewed as a special case within optimal-control theory, then one set of necessary conditions is obtained. If it is viewed as an extension of classical parameter- optimization theory, then a different set of necessary conditions are obtained. We show here that the two sets of necessary conditions are, in fact, equivalent. However, numerical utilization of the conditions differ significantly with respect to difficulty in obtaining a solution. The necessary conditions obtained from parameter-optimization theory are generally easier to implement. This latter observation is demonstrated with the aid of two examples. One example involves environmental adaptation of annual plants, and the other involves constant-rate harvesting of a prey-predator system.