The bang-bang principle

Abstract

The aim of this survey is to present a framework in which statements that a control leading to a desired effect takes its values fromextreme points of the admissible set can be expressed in a concise and unified manner. We emphasize results concerning systems with infinite-dimensional space of states. Almost no attention is paid to the history of the subject. The list of references is by no means exhaustive or even indicative about the literature concerning the subject. The inclusion or otherwise of an item in no way represents our reflection on its importance. Possibly, by following the references in the quoted works, a better picture about the history of the subject can be obtained. A more serious omission, dictated by the limitations of the space and time, is the fact that deeper applications are not discussed. For example, the description of effective methods for numerical calculation of optimal controls based on their taking on as values the extreme points of the admissible set would be impracticable in an article of this scope. However, we wish to stress that it is mainly because of the nontraditional applications that the theme of this survey is so interesting and attractive.