It is well-known that linear dynamical systems with Gaussian noise and
quadratic cost (LQG) satisfy a separation principle. Finding the optimal
controller amounts to solving separate dual problems; one for control and one
for estimation. For the discrete-time finite-horizon case, each problem is a
simple forward or backward recursion. In this paper, we consider a
generalization of the LQG problem in which there are two controllers. Each
controller is responsible for one of two system inputs, but has access to
different subsets of the available measurements. Our paper has three main
contributions. First, we prove a fundamental structural result: sufficient
statistics for the controllers can be expressed as conditional means of the
global state. Second, we give explicit state-space formulae for the optimal
controller. These formulae are reminiscent of the classical LQG solution with
dual forward and backward recursions, but with the important difference that
they are intricately coupled. Lastly, we show how these recursions can be
solved efficiently, with computational complexity comparable to that of the
centralized problem.

本文研究了具有两个控制器的广义线性动态系统问题，证明了控制器的充分统计量可以表示为全局状态的条件均值，并给出了最优控制器的具体状态空间公式，以及如何高效解决此问题的算法，其计算复杂度可与集中式问题相媲美。