Controllability of right invariant systems on real simple Lie groups

✍ Scribed by J.P. Gauthier; I. Kupka; G. Sallet

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 190 KB
• Volume: 5
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(84)80101-2

✦ Synopsis

We exhibit some classes of Lie groups, and a set of open assumptions on these groups, such that, under these assumptions, the 'controllability rank condition' becomes a necessary and sufficient condition for controllability of right invariant systems.

condition when .L#(A, B), the Lie algebra generated by A and B, is equal to L, the Lie algebra of G.

For a family of vector fields of the form (1), we say that a set of assumptions is open if the set of couples (A, B) for which they are satisfied is an open subset of L × L.

We will exhibit some classes of Lie groups, and a set of open assumptions on these groups, such that the controllability rank condition becomes, under these assumptions, a necessary and sufficient condition for controllability.

In Section 2 we state a few definitions, and the main result. In Section 3 we give the proof of the result.

As suggested by the referee, in our appendix, we explain some of the Lie-theoretic concepts we are using in our paper.