Average tracking consensus of multi-agent systems under denial-of-service attacks and delay via a dynamic quantization mechanism and the numerical simulations to spacecraft formation

In this article, the average tracking consensus problem of multi-agent systems (MASs) with denial-of-service(DoS) attacks and time-varying delays via a dynamic quantized control is investigated. First, an auxiliary detector incorporating internal variables is designed for each agent to track the average signals relying on topological structure of MASs. The dynamic quantization mechanism is designed for the quantizer, which can avoid saturation and eliminate the quantization error asymptotically. Then, we rigorously prove that the proposed dynamic quantization mechanism can handle general linear MASs with constrained bandwidth of digital communication network. Furthermore, we extend the quantization framework to guarantee average tracking consensus even under simultaneous DoS attacks and time-varying delays. By constructing appropriate Lyapunov functions and employing mathematical recursion, we derive sufficient conditions concerning constrained bandwidth, DoS attacks and time-varying delays. Finally, a practical example of spacecraft formation tracking in low Earth orbit is presented to validate the theoretical conclusions of this study.