Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem

A decentralized control problem involving K nodes is formulated. At each node are sensors and controls. The object is to share the information of each sensor, processed with a Kalman estimator, with all the other nodes so that the controllers can be computed using the best estimate of the state of the system given the information from all the sensors. The controls are determined so that the expected value of a quadratic performance index is minimized. The problem is formulated as a decentralized control problem without a central supervisor so that the system performance will degrade gracefully under structural perturbations, Therefore, the transmission of data is from each node to every other node: there are Σi=1 K (i-1) links connecting all nodes. It is shown that if the dimension of the controls at each node l is less than both the dimension of the data at node m and the dimension of the state, then a data vector with dimension of the control at l can be transmitted from m to l. This compression of data transmission is done at the expense of propagating an additional data dependent vector at each node beyond the usual Kalman filter equations.