  In this paper, we propose a distributed differentially private receding
horizon control (RHC) approach for multi-agent systems (MAS) with metric
temporal logic (MTL) specifications. In the MAS considered in this paper, each
agent privatizes its sensitive information from other agents using a
differential privacy mechanism. In other words, each agent adds privacy noise
(e.g., Gaussian noise) to its output to maintain its privacy and communicates
its noisy output with its neighboring agents. We define two types of MTL
specifications for the MAS: agent-level specifications and system-level
specifications. Agents should collaborate to satisfy the system-level MTL
specifications with a minimum probability while each agent must satisfy its own
agent-level MTL specifications at the same time. In the proposed distributed
RHC approach, each agent communicates with its neighboring agents to acquire
their noisy outputs and calculates an estimate of the system-level trajectory.
Then each agent synthesizes its own control inputs such that the system-level
specifications are satisfied with a minimum probability while the agent-level
specifications are also satisfied. In the proposed optimization formulation of
RHC, we directly incorporate Kalman filter equations to calculate the estimates
of the system-level trajectory, and we use mixed-integer linear programming
(MILP) to encode the MTL specifications as optimization constraints. Finally,
we implement the proposed distributed RHC approach in a case study.
