Optimal control and quasi-velocities

Abstract

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinemactic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelarations. Formulating the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently [48]. We also provide several examples to illustrate our construction