This paper deals with dynamic quantized consensus of dynamical agents in a general form under packet losses induced by Denial-of-Service (DoS) attacks. The communication channel has limited bandwidth and hence the transmitted signals over the network are subject to quantization. To deal with agent's output, an observer is implemented at each node. The state of the observer is quantized by a finite-level quantizer and then transmitted over the network. To solve the problem of quantizer overflow under malicious packet losses, a zooming-in and out dynamic quantization mechanism is designed. By the new quantized controller proposed in the paper, the zooming-out factor is lower bounded by the spectral radius of the agent's dynamic matrix. A sufficient condition of quantization range is provided under which the finite-level quantizer is free of overflow. A sufficient condition of tolerable DoS attacks for achieving consensus is also provided. At last, we study scalar dynamical agents as a special case and further tighten the zooming-out factor to a value smaller than the agent's dynamic parameter. Under such a zooming-out factor, it is possible to recover the level of tolerable DoS attacks to that of unquantized consensus, and the quantizer is free of overflow.

翻译：本文研究一般形式动态智能体在拒绝服务攻击导致的数据包丢失下的动态量化一致性问题。通信信道带宽有限，因此网络上传输的信号需经过量化处理。为处理智能体输出，每个节点实现一个观测器。观测器状态经有限级量化器量化后通过网络传输。为解决恶意数据包丢失下的量化器溢出问题，设计了一种动态缩放量化机制。通过本文提出的新型量化控制器，缩放因子下限由智能体动态矩阵的谱半径决定。给出了量化范围的充分条件，确保有限级量化器无溢出。同时提供了实现一致性的可容忍拒绝服务攻击的充分条件。最后，以标量动态智能体为特例，将缩放因子进一步收紧至小于智能体动态参数的值。在该缩放因子下，可恢复至与未量化一致性相同的拒绝服务攻击容忍水平，且量化器无溢出。