Distributed Differentially Private Control Synthesis for Multi-Agent Systems with Metric Temporal Logic Specifications

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. 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 while each agent must satisfy its own agentlevel MTL specifications at the same time. In the proposed distributed RHC approach, each agent communicates with its neighboring agents to acquire their estimate of the system-level trajectory and updates its estimate of the system-level trajectory. Then, each agent synthesizes its own control inputs such that the system-level specifications are satisfied with a probabilistic guarantee while the agent-level specifications are also satisfied with a deterministic guarantee. In the proposed optimization formulation of RHC, we directly incorporate Kalman filter equations to calculate the system-level trajectory estimates. We use mixed-integer linear programming (MILP) to encode the MTL specifications as optimization constraints. Finally, we implement the proposed distributed RHC approach in two scenarios.