Coordinated One-Step Optimal Distributed State Prediction for a Networked Dynamical System

A new recursive one-step state prediction procedure is derived for a networked dynamic system. Under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters, this predictor estimates plant's local states based only on local system output measurements. This estimator can be easily realized in a distributed way, and can also be simply scaled to systems with a large amount of subsystems, provided it has enough communication and storage capacities. It is proved that when prediction error variances are adopted in performance comparisons, the optimal gain matrix is usually unique. Recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors. The optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known Kalman filter utilizing only local system output measurements, which makes it possible to robustify this state predictor using a sensitivity penalization approach. Numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped Kalman filter.