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.

本文提出了一种基于预测状态表征（PSRs）的离散时间动态系统模型，其主要思想是将系统的状态表示为可观测实验结果的预测，同时通过系统动力学矩阵来推导 PSRs，并证明了 PSRs 比 nth-order Markov 模型和 HMMs/POMDPs 更为通用，最后讨论了 PSRs 和 OOMs 之间的区别，并给出了未来工作的方向。