Active Inference and Functional Parametrisation: Differential Flatness and Smooth Random Realisation

This paper is a first attempt to marry constructive nonlinear control theory techniques with active inference. Specifically, we are interested in the relationship between differential flatness and the design of generative models for use in control settings. We place specific emphasis on the pathwise properties of differentially flat systems that inherit from their definition in terms of successive temporal derivatives and relate this to the use of generalised coordinates of motion in formulating continuous-time generative models in active inference. To illustrate the basic concepts, we appeal to the example of oculomotor control.