Any dynamical system is fully accessible through one single actuator, and related problems
Résumé
Whether an autonomous system can be rendered fully accessible through one single actuator is a long standing open problem which got some solutions in special cases when additional constraints are considered. Herein it is shown that a solution to the general problem is provided as an easy consequence of the straightening theorem. This solution is innovative for linear time-invariant systems as well and relaxes the well known cyclicity condition as it involves nonlinear state transformations. The dual problem of designing one single sensor to render a given system observable gets a similar almost unconditional solution.