Any dynamical system is fully accessible through one single actuator and related problems

Abstract

Summary 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 obtains a similar almost unconditional solution.