Synchronization of discrete-time multi-agent systems under input sets with limited precision

Abstract

Purpose – This paper aims to study that for multi-agent systems, how to find proper control protocols to ensure synchronization when the input set of each agent is not the whole real axis but a discrete set, and how the coarseness of imprecise input sets affect the synchronization control of the multi-agent systems. Design/methodology/approach – The paper uses a relative state feedback method and non-linear mapping functions to design a proper control protocol which matches the coarseness of the input set and ensures synchronization. For theoretical analysis, the paper uses an error analysis method and mathematic induction to prove the effectiveness of the designed control protocol. The paper also uses a numerical example to show the correctness of the theoretical results. Findings – The paper provides a method for protocol design when the input set of each agent is imprecise. The paper establishes a bi-direction relationship which suffices for synchronization between the coarseness of the input set and the synchronization precision, and finds that this relationship describes how the coarseness of the input set affects the synchronization control of the multi-agent system. Research limitations/implications – This paper only studies the case with logarithmically distributed and uniformly distributed discrete input sets. The authors are encouraged to study the synchronization control of multi-agent systems under input sets with more general distributions. Practical implications – The paper includes implications for coordination control of multi-agent networks when the actuator of each agent is with a limited capacity, which leads to the case of discrete input sets with limit precision. Originality/value – This paper fulfils an identified need to study how the coarseness of the input set of each agent affects the synchronization control of the whole multi-agent system.