  Although there are many neural network (NN) algorithms for prediction and for
control, and although methods for optimal estimation (including filtering and
prediction) and for optimal control in linear systems were provided by Kalman
in 1960 (with nonlinear extensions since then), there has been, to my
knowledge, no NN algorithm that learns either Kalman prediction or Kalman
control (apart from the special case of stationary control). Here we show how
optimal Kalman prediction and control (KPC), as well as system identification,
can be learned and executed by a recurrent neural network composed of
linear-response nodes, using as input only a stream of noisy measurement data.
  The requirements of KPC appear to impose significant constraints on the
allowed NN circuitry and signal flows. The NN architecture implied by these
constraints bears certain resemblances to the local-circuit architecture of
mammalian cerebral cortex. We discuss these resemblances, as well as caveats
that limit our current ability to draw inferences for biological function. It
has been suggested that the local cortical circuit (LCC) architecture may
perform core functions (as yet unknown) that underlie sensory, motor,and other
cortical processing. It is reasonable to conjecture that such functions may
include prediction, the estimation or inference of missing or noisy sensory
data, and the goal-driven generation of control signals. The resemblances found
between the KPC NN architecture and that of the LCC are consistent with this
conjecture.
