Optimal Synchronization for Networks of Noisy Double Integrators

• Published in: IEEE transactions on automatic control Vol. 56; no. 5; pp. 1146 - 1152
• Main Authors: Carli, R, Chiuso, A, Schenato, L, Zampieri, S
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Clocks; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Double integrators; Eigenvalues and eigenfunctions; Exact sciences and technology; Graphs; Networked control systems; Networks; Noise; Optimization; Optimized production technology; Protocols; Software; Strategy; Studies; Synchronism; Synchronization; wireless sensor networks; Additive noise; Networked control systems; wireless sensor networks; Connected graph; Randomized algorithm; Clock; Synchronization; Modeling; Steady state; Discrete time; Distributed control; Integrator; Wireless network; Communication graph; Sensor array; Non directed graph
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2107051

In this technical note, we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are nonidentical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds are nonidentical and are subject to variations. This synchronization protocol is formally studied in its synchronous implementation. In particular, we provide a completely distributed strategy that guarantees convergence for any undirected connected communication graph and we also propose an optimal design strategy when the underlaying communication graph is known. Moreover, this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations including also randomized implementation of the proposed algorithm are presented.