Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop

• Published in: IEEE transactions on automatic control Vol. 53; no. 5; pp. 1311 - 1317
• Main Author: Schenato, L.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Architecture; Communications networks; Computer architecture; Computer science; control theory; systems; Control theory. Systems; Covariance; Delay; Delay estimation; Digital communication; Errors; Estimators; Exact sciences and technology; Kalman filter; Linear systems; Loss measurement; Mathematical analysis; minimum variance estimator; Modelling and identification; Networked control systems; Optimal control; Optimization; packet drop; Process control. Computer integrated manufacturing; random time delay; Sensor systems; Sensors; State estimation; Steady-state; Stochastic processes; Studies; Performance evaluation; Error estimation; Finite memory; Kalman filter; Optimal estimation; Optimization; Time varying system; Covariance; Observer; Digital communication; Delay time; random time delay; System identification; minimum variance estimator; Lower bound; Sampled system; Probabilistic approach; Measurement sensor; Transmission protocol; Buffer memory; Distributed system; Communication network; Steady state; Upper bound; Minimal variance; Linear system; Optimal control; packet drop; Distributed control; networked control systems; Transmission loss
• DOI: 10.1109/TAC.2008.921012
• ISSN: 0018-9286

In this note, we study optimal estimation design for sampled linear systems where the sensors measurements are transmitted to the estimator site via a generic digital communication network. Sensor measurements are subject to random delay or might even be completely lost. We show that the minimum error covariance estimator is time-varying, stochastic, and it does not converge to a steady state. Moreover, the architecture of this estimator is independent of the communication protocol and can be implemented using a finite memory buffer if the delivered packets have a finite maximum delay. We also present two alternative estimator architectures that are more computationally efficient and provide upper and lower bounds for the performance of the time-varying estimator. The stability of these estimators does not depend on packet delay but only on the overall packet loss probability. Finally, algorithms to compute critical packet loss probability and estimators performance in terms of their error covariance are given and applied to some numerical examples.