Nilpotent control systems (Q700048)

The authors analyse the application of the filiform graded Lie algebras [\textit{M. Vergne}, Bull. Soc. Math. France 78, 98-116 (1970; Zbl 0244.17011)] to control theory. In this context, the model filiform algebra \(L_{n}\) corresponds to a mobile robot on the plane, and the system corresponding to the graded algebra \(Q_{n}\) and its controllability are discussed. This case is related to the former via deformation theory of Lie algebras.