| 内容提要: |
In communications, unknown variables are usually
modelled as random variables, and concepts such as independence,
entropy and information are defined in terms of the underlying
probability distributions. In contrast, control theory often treats
uncertainties and disturbances as bounded unknowns having no
statistical structure. The area of networked control combines both
fields, raising the question of whether it is possible to construct
meaningful analogues of stochastic concepts such as independence,
Markovness, entropy and information without assuming a probability
space. This paper introduces a framework for doing so,
leading to the construction of a maximin information functional for
nonstochastic variables. It is shown that the largest maximin information
rate through a memoryless, error-prone channel in this
framework coincides with the block-coding zero-error capacity of
the channel.Maximin information is then used to derive tight conditions
for uniformly estimating the state of a linear time-invariant
system over such a channel, paralleling recent results of Matveev
and Savkin. |