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I have a state-space model of a greenhouse control model that I'd like to transform into a probabilistic graphical model (to make it easier for non-technical managers to understand relationships among variables than the formula-based state-space model).

What is the most specific graphical model formalism that is still general enough to model a non-linear continuous state space model?

What have I tried so far

I started down the path of Influence Diagrams (being attracted to the identification of decision nodes and utility functions) but found the need to identify causality among the variables as a bit cumbersome. This Scholarpedia article seems to imply that state space models are another name for Hidden Markov Models, whereas the Barber text seems to place state-space models as a special form of continuous latent Markov Models (reserving Hidden Markov Models as a term used for discrete latent models).

I'd like to make sure that the time invested in modeling variable relationships as a graphical model isn't wasted using the wrong formalism.

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