Differentially private formation control: Privacy and network co-design

Privacy in multi-agent control is receiving increased attention, though often a networked system and privacy protections are designed separately, which can harm performance. Therefore, this paper presents a co-design framework for networks and private controllers, and we apply it to private formation control. Agents' state trajectories are protected using differential privacy, and we quantify its impact by bounding the steady-state error for private formations. Then, we analyze tradeoffs between privacy level, system performance, and connectedness of the network's communication topology. These tradeoffs are used to formulate a co-design optimization framework to jointly design agents' communication topology and their privacy levels. Simulation results illustrate the success of this framework.