Quantized Consensus under Data-Rate Constraints and DoS Attacks: A Zooming-In and Holding Approach

This paper is concerned with the quantized consensus problem for uncertain nonlinear multi-agent systems under data-rate constraints and Denial-of-Service (DoS) attacks. The agents are modeled in strict-feedback form with unknown nonlinear dynamics and external disturbance. Extended state observers (ESOs) are leveraged to estimate agents' total uncertainties along with their states. To mitigate the effects of DoS attacks, a novel dynamic quantization with zooming-in and holding capabilities is proposed. The idea is to zoom-in and hold the variable to be quantized if the system is in the absence and presence of DoS attacks, respectively. The control protocol is given in terms of the outputs of the ESOs and the dynamic-quantization-based encoders and decoders. We show that, for a connected undirected network, the developed control protocol is capable of handling any DoS attacks inducing bounded consecutive packet losses with merely 3-level quantization. The application of the zooming-in and holding approach to known linear multi-agent systems is also discussed.