Differentially Private Controller Synthesis with Metric Temporal Logic Specifications

Privacy is an important concern in various multi-agent systems in which data collected from the agents are sensitive. We propose a differentially private controller synthesis approach for multi-agent systems subject to high-level specifications expressed in metric temporal logic (MTL). We consider a setting where each agent sends data to a cloud (computing station) through a set of local hubs and the cloud is responsible for computing the control inputs of the agents. Specifically, each agent adds privacy noise (e.g., Gaussian noise) point-wise in time to its own outputs before sharing them with a local hub. Each local hub runs a Kalman filter to estimate the state of the corresponding agent and periodically sends such state estimates to the cloud. The cloud computes the optimal inputs for each agent subject to an MTL specification. While guaranteeing differential privacy of each agent, the controller is also synthesized to ensure a probabilistic guarantee for satisfying the MTL specification. We provide an implementation of the proposed method on a simulation case study with two Baxter-On-Wheels robots as the agents.