Groupoids in Control Systems and the Reachability Problem for a Class of Quantized Control Systems with Nonabelian Symmetries

The aim of this paper is twofold. On one hand we present an approach to the general problem of nonlinear control in the framework of (differentiable) groupoids, which, in our opinion deserves further investigation. On the other hand, using recently-developed algebraic tools, we show that for a control system whose state space is a semisimple Lie group (like SO(3)), it is possible to reach a dense subset of the state space using just two properly chosen discrete controls, and this property is robust with respect to the choice of controls.

• Type: Conference
• Year: 2007
• Where: HYBRID
• Authors: Alessandro Arsie, Emilio Frazzoli
• Keywords: HYBRID 2007, Hybrid Systems, Nonlinear Control, Semisimple Lie Group, State Space