Metrics to compare and control dynamical systems

The focus of this paper is on similarity based controller selection, which is thought of as an essential component of cognitive control. The strength of cognitive systems lies in the ability to compare the current situation with previously experienced situations. This allows for an efficient reuse of previously successful solutions. Transferring this motivation to control theory requires a distance measure between dynamical systems. Given a new dynamical system, it is then possible to find the closest previously controlled system and reuse the corresponding controller. This paper highlights four distance measures and analyzes their suitability for similarity based controller selection. The compared distance measures are Multiple Models Adaptive Control, the Binet-Cauchy kernels, the Martin distance and the ν-gap metric.