Symmetries and Minimal Flat Outputs of Nonlinear Control Systems

Abstract

Consider a nonlinear control system of the form $\Pi : \dot{x}=F(x,u)$, where $x \in X$, a smooth n-dimensional manifold and $u\in U$, a smooth m-dimensional manifold. To the system Π we associate its field of admissible velocities $\mathcal{F}(x)=\{F(x, u): u \in U\} \subset T_xX$. We will say that a diffeomorphism of the state space X is a symmetry of Π if it preserves the field of admissible velocities.

Dedicated to Professor Arthur J. Krener on the occasion of his 60th birthday.