ABSTRACT
The proofs of all theorems quoted in this paper can be found in the forthcoming book titled Geometric Control Theory by V. Jurdjevic, (to appear in Studies in Advanced Mathematics, Cambridge University Press.) The material for this article is taken out of the first part of the book dealing with the reachable sets of Lie determined systems (which includes analytic systems). The reader may also find some of this material in the following publications:
1. Jurdjevic, V. and Kupka, I.A., Polynomial control system, Math. Ann., 361-368, 1985. 2. Jurdjevic, V. and Sussmann, H.J., Control systems on Lie groups, J. Diff. Eqs., 12, 313-329, 1972. 3. Sussmann, H.J. and Jurdjevic, V., Controllability of non-linear systems, J. Diff. Eqs., 12, 95-116,
Convexification of control systems is also known as the relaxation of controls in the early literature on control. See for instance,
4. Hermes, H. and LaSalle, J.P., Functional Analysis and Time Optimal Control, Academic Press, New York, 1969.
