Control Theoretic Models of Human Drivers in Car Following

Abstract

This paper is concerned with mathematical models of the control behavior of human drivers while following another vehicle in single lane traffic. The emphasis is on the representation of the individual driver, rather than on such abstract parameters of multi-lane traffic as average density or average velocity. Three basic types of approaches to representing the driver's control strategy are reviewed. First is a classical control structure in which assumptions concerning the stimulus-response characteristics of the driver are included, and a form for his control strategy algorithm is assumed. The second class of models is based on optimal control theory. The major feature of this class of models is that an assumed performance index is explicitly included in the formulation, so that the driver's control strategy arises as a result of his attempts to minimize this index or criterion. The third class of models reviewed in the paper are heuristic models, which arise from control theory. The first of these, termed the “look-ahead” model, is based on the assumption that the driver is capable of observing more than one car ahead of him, and that he adjusts his own strategy from an analysis of the behavior of a majority of the vehicles he perceives. The second of these heuristic models is a finite state structure which is developed from the hypothesis that the driver attempts at all times to maintain a velocity equal to that of the lead car along with a safe headway. The paper concludes with a brief discussion of some current areas of research and possible applications.