用量化控制分析多智能体的一致性问题. 不同于以往的静态量化器, 例如均匀量化或者对数量化, 文章运用动态~Sigma-Delta~($\mathit{\Sigma }\mathrm{\Delta }$) 量化器提出新的多智能体量化一致性协议, 利用有限比特数使系统达到渐进一致, 且渐进收敛到初值的平均值, 并且给出系统达到渐进一致的充分条件. 与静态的非对称和对称量化器相比, $\mathit{\Sigma }\mathrm{\Delta }$ 量化器克服了静态量化器无记忆并且不能消除稳态误差及需要无限比特的量化信息的缺点, 体现了它的优越性.

This paper develops a framework for treating multi-agent consensus problems using quantized control. Unlike the previous static quantizer, such as uniform quantizer or logarithm quantizer, this paper proposes a new quantized consensus protocol through dynamic $\mathit{\Sigma }\mathrm{\Delta }$ quantizer for multi-agent dynamical systems, which makes the system achieve asymptotic consensus with finite bits and converge to the average of the initial states. Moreover, the sufficient condition is given. Compared with the asymmetrically and symmetrically quantizer, $\mathit{\Sigma }\mathrm{\Delta }$ quantizer overcomes the disadvantages of the no memory and the existence of the steady state error about the static quantizer and the need of quantification with unlimited bits of information, which reflects its advantage.