Coding scheme based on boundary function for consensus control of multi-agent system with time-varying topology

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Abstract
The relationship between control and communication is becoming more and more important in multi-agent system. Besides consensus protocol, the coding scheme is also a part of the system design. In this study, the boundary function method is proposed for the coding scheme design to solve quantised consensus problem of multi-agent system under channels with time-varying connected topology. Two cases of channels with time-varying topology are considered: (i) channels connecting agents (controllers) and actuators and (ii) channels connecting neighbouring agents. To obtain convergence conditions for consensus problems, a relation between incidence matrices of any two connected graphs is used for the first case and an expression of the boundary function is developed for the second case. Since the quantiser is parameterised by the boundary function and the channel data rate, constraint expressions that include the channel data rate and the system convergence rate are obtained to show the tradeoff between control and communication performances.

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