Linear Optimal Control on Factor Graphs — A Message Passing Perspective —

Factor graphs form a class of probabilistic graphical models representing the factorization of probability density functions as bipartite graphs. They can be used to exploit the conditional independence structure of the underlying model to efficiently solve inference problems by message passing. The present paper advocates the use of factor graphs in control and highlights similarities to, e. g., signal processing and communications where this class of models is widely used. By applying the factor graph framework to a probabilistic interpretation of optimal control, several classical results are recovered. The dynamic programming approach to linear quadratic Gaussian control is described as a message passing algorithm on factor graph on which possible extensions are exemplified. A factor graph-based iterative learning control scheme is outlined and an expectation maximization-based estimation of normal unknown variance priors is adapted for the derivation of sparse control signals, highlighting the benefits of using a unified framework across disciplines by mixing and matching corresponding graphical algorithms.