Distributed Consensus With Limited Communication Data Rate

• Published in: IEEE transactions on automatic control Vol. 56; no. 2; pp. 279 - 292
• Main Authors: TAO LI, MINYUE FU, LIHUA XIE, ZHANG, Ji-Feng
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Asymptotic properties; Average-consensus; communication energy; Communication system control; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control systems; Convergence; data rate; Direct power generation; distributed consensus; Distributed control; distributed coordination; distributed estimation; Eigenvalues; Eigenvalues and eigenfunctions; Energy conservation; Exact sciences and technology; Laboratories; Mathematics; multi-agent systems; Networks; Protocol (computers); Protocols; Quantization; sensor network; Software; Space technology; Studies; Energy consumption; Total energy; multi-agent systems; Quantization; Data transmission; data rate; communication energy; Eigenvalue problem; Average-consensus; Numerical convergence; Information exchange; State constraint; distributed consensus; distributed estimation; Coordination; Minimization; Decoding; Consensus; Multiagent system; sensor network; Time average; Discrete time; Distributed control; Asymptotic approximation; Causality; Sensor array; distributed coordination
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2052384

Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multi-agent networks. Although many proposed average-consensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits of information are necessary for each pair of adjacent agents to exchange at each time step to ensure average consensus? In this paper, we consider average-consensus control of undirected networks of discrete-time first-order agents under communication constraints. Each agent has a real-valued state but can only exchange symbolic data with its neighbors. A distributed protocol is proposed based on dynamic encoding and decoding. It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. An explicit form of the asymptotic convergence rate is given. It is shown that as the number of agents increases, the asymptotic convergence rate is related to the scale of the network, the number of quantization levels and the ratio of the second smallest eigenvalue to the largest eigenvalue of the Laplacian of the communication graph. We also give a performance index to characterize the total communication energy to achieve average consensus and show that the minimization of the communication energy leads to a tradeoff between the convergence rate and the number of quantization levels.