Controllability asks whether a system can be driven from its present state to a target state, within finite time, by using the inputs the system permits. A greenhouse sensor may accurately report 35°C. Yet if the equipment includes only a heater, with no ventilation, shade or cooling, the operator cannot actively reach 25°C using the available input, however clearly the need is understood.
Controllability differs from observability. Observability asks whether external signals let us infer an internal state; controllability asks whether there is an effective channel for changing that state. It is also more specific than reachability in the general sense: the target may exist while present actuators, permissions and time still make it inaccessible.
The concept reminds us that control is not strong intention or repeated commands. It is a relation among the target, the system's dynamics and its available inputs. More sensors can improve knowledge without increasing control. An input that acts in the missing direction can genuinely enlarge the controllable range.
https://ocw.mit.edu/courses/6-832-underactuated-robotics-spring-2009/resources/lecture-6-acrobot-and-cart-pole/
https://ntrs.nasa.gov/citations/19700032148
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