  Modeling dynamical systems, both for control purposes and to make predictions
about their behavior, is ubiquitous in science and engineering. Predictive
state representations (PSRs) are a recently introduced class of models for
discrete-time dynamical systems. The key idea behind PSRs and the closely
related OOMs (Jaeger's observable operator models) is to represent the state of
the system as a set of predictions of observable outcomes of experiments one
can do in the system. This makes PSRs rather different from history-based
models such as nth-order Markov models and hidden-state-based models such as
HMMs and POMDPs. We introduce an interesting construct, the systemdynamics
matrix, and show how PSRs can be derived simply from it. We also use this
construct to show formally that PSRs are more general than both nth-order
Markov models and HMMs/POMDPs. Finally, we discuss the main difference between
PSRs and OOMs and conclude with directions for future work.
