Application of Linear Control Theory to a Simple Cognitive Model of Controlled Processing: A Case Study

Cognitive effort is a defining feature of cognitive control but theories about its origin and purpose have long been controversial. Recently, it has been proposed that cognitive effort can be understood using linear control theory (LCT), a mathematical formalism developed in the engineering literature to control dynamical systems. On this view, effort levels reflect the energy required by the cognitive control system to support representational states that deviate from the intrinsic dynamics of the cognitive system. Although LCT holds promise for elucidating a range of effort-related processes such as working memory and task switching, the technique is likely unfamiliar to many cognitive psychologists. Therefore, to introduce the approach to a broader audience, here we apply LCT to a classic computational model of cognitive control: Cohen et al.’s (1990) artificial neural network model of the Stroop task. In so doing, this study serves as a tutorial on the application of control theoretic principles to models of cognitive control and their associated effort costs.