Where does controllability collide?

Kalman's 1960 On the general theory of control systems introduced controllability as a property of a dynamical system written in terms of state variables: the system is controllable if some choice of inputs can drive it from any starting state to any desired state in a finite time. Kalman's 1963 Mathematical description of linear dynamical systems gave the algebraic test for this in linear systems and paired it with observability. The referent is a formal property of a set of equations of motion, a yes-or-no fact about whether the inputs can reach every state, and it has nothing to do with a person judging who was responsible for an outcome or with how frightening a hazard feels.[1][2]

Unit

A yes-or-no property of a state-space system, sometimes graded by the rank of its controllability matrix

Recovery means

Not applicable

Measured by

Tested algebraically; for a linear system by checking that its controllability matrix has full rank

Fischhoff, Slovic, Lichtenstein, Read, and Combs's 1978 How safe is safe enough? introduced controllability as one of the characteristics people use to judge a hazard: it captures whether a person feels able to avoid harm from an activity through their own skill or care, as with driving a car versus a distant industrial accident. Slovic's 1987 Perception of risk mapped it as part of the dread cluster that helps explain why some low-probability hazards provoke strong public concern. The referent is a felt attribute of a hazard reported on rating scales, and it differs from an equation's reachable states and from a judgment about who caused a single outcome.[3][4]

Unit

A rating of one hazard on a scale from controllable to uncontrollable

Recovery means

Not applicable

Measured by

Elicited by having respondents rate hazards from controllable to uncontrollable, then reduced by factor analysis into risk dimensions

Weiner's 1979 A theory of motivation for some classroom experiences named controllability as a third dimension of causal attribution, alongside where the cause is located and whether it is stable: it marks whether the cause of an outcome, such as the effort behind a failed exam, was under the person's volitional control. Weiner's 1985 An attributional theory of achievement motivation and emotion tied this dimension to social emotions like anger, guilt, and pity and to expectations about the future. The referent is a perceived quality of the cause of a specific outcome as judged by a person, and it is unrelated to whether a machine's inputs can reach every state or to how controllable a whole class of hazards feels.[5][6]

Unit

A classification of one outcome's perceived cause as controllable or uncontrollable

Recovery means

Not applicable

Measured by

Assessed by coding or rating causal explanations on a controllable-to-uncontrollable dimension, often with the Causal Dimension Scale