Controllability with unilateral control inputs

Many control systems contain control inputs which are constrained to be non–negative. Unfortunately, the unilateral nature of such inputs makes them similar to a drift term, and correspondingly complicates any attempt to determine controllability. We present a controllability test in which Lie brackets are characterized as “good ” or “bad, ” from which controllability follows from the relationship between these “good ” and “bad” brackets. This test is relatively straightforward to apply and its application is illustrated with an example.