Dynamic model dependency for a decentralized linear-quadratic-Gaussian control problem

A decentralized control problem is considered with sensors, controls, and local Kalman estimators at each node for independence and redundancy. Controls using the best estimate of the system state, are sought to minimize a quadratic performance index. It is noted that cross-correction between the nodal estimates due to process noise in the dynamics model must be considered for proper fusion of the estimates. The authors demonstrate the underestimation of the control error variance from neglecting estimate cross correlation via the rendezvous problem for the linear quadratic (LQ) regulator or the fight path control problem for the LQ tracker dynamic models. When steady-state Kalman filters can be used, the calculation and information requirements are significantly reduced. The underestimation of the control error variance is shown to be nonnegligible at high gain values for these filters for each of the dynamics models considered in the rendezvous problem