A geometric isomorphism with applications to closed loop controls

Summary form only given. In this work feedback equivalence of n-state, (n-1)-control systems satisfying certain regularity conditions divides such systems into two invariant classes. The author shows that class 1 corresponds, via a geometric isomorphism, to classical Lagrangian variational problems. He proves the existence of time-critical closed-loop controls for systems which satisfy the nondegeneracy condition that the analog of the Hessian for the Lagrangian problem have full rank. The author shows that the vanishing of this Hessian characterizes the control linear systems in class 1 and identifies the rank condition for local controllability for such systems as the nonvanishing of a differential invariant. The control linear systems in class 2 are also characterized by the vanishing of an invariant, and the rank condition is identified