Vehicle dynamics applications of optimal control theory

The aim of the paper is to survey the various forms of optimal-control theory which have been applied to automotive problems and to present illustrative examples of applications studies, with assessments of the state of the art and of the contributions made through the use of optimal-control ideas. After a short introduction to the topic mentioning several questions to which optimal-control theory has been addressed, brief reviews of automotive-applicable optimal-control theory are given. There are outlines of the Linear Quadratic Regulator, without and with state reconstruction and then with the addition of disturbance preview, the nonlinear regulator or state-dependent-Riccati equation method, general numerical optimal-control theory including indirect and direct methods, model predictive control and robust control. Applications of the theory to active and semi-active suspension design and performance, worst-case manoeuvring, minimum-time manoeuvring and high-quality driving are then discussed in detail. Application sections describe the problem, the theory that has been used, what has been discovered and what remains to be found. The record of optimal-control theory in aiding the understanding of the various issues, in helping with system designs and knowledge of what is possible, and in guiding future research is assessed. Some ideas about future work are included.