  The application of distributed model predictive controllers (DMPC) for
multi-agent systems (MASs) necessitates communication between agents, yet the
consequence of communication data rates is typically overlooked. This work
focuses on developing stability-guaranteed control methods for MASs with
limited data rates. Initially, a distributed optimization algorithm with
dynamic quantization is considered for solving the DMPC problem. Due to the
limited data rate, the optimization process suffers from inexact iterations
caused by quantization noise and premature termination, leading to sub-optimal
solutions. In response, we propose a novel real-time DMPC framework with a
quantization refinement scheme that updates the quantization parameters on-line
so that both the quantization noise and the optimization sub-optimality
decrease asymptotically. To facilitate the stability analysis, we treat the
sub-optimally controlled MAS, the quantization refinement scheme, and the
optimization process as three interconnected subsystems. The cyclic-small-gain
theorem is used to derive sufficient conditions on the quantization parameters
for guaranteeing the stability of the system under a limited data rate.
Finally, the proposed algorithm and theoretical findings are demonstrated in a
multi-AUV formation control example.
