A conjecture concerning certain notions of controllability for a class of uncertain systems

Abstract

This note deals with two notions of controllability which arise in dynamical systems whose descriptions include unknown but bounded parameters. Roughly speaking, exact controllability involves steering an initial state of the system to a prescribed target set X in a guaranteed sense; that is, no matter what uncertainty occurs, the state will be transferred to the target. Approximate controllability involves steering an initial state of the system, also in a guaranteed sense, to within any given distance ε of the target set. After formally defining these notions of controllability, it is conjectured that these notions of exact and approximate controllability are equivalent. Some special cases are described for which the truth of the conjecture can be readily verified. Show more