Some applications of quasi-velocities in optimal control
For researchers in geometric mechanics and control theory, this provides a theoretical unification but is incremental.
This paper studies optimal control problems for nonholonomic systems on Lie algebroids using quasi-velocities, providing a unified framework that explains recent results. It includes examples but reports no quantitative results.
In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, 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 accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction.