# A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics

## TL;DR

This paper introduces a system-theoretic framework called dynamical privacy for protecting initial states in multiagent systems by using local, time-varying output masks that asymptotically reveal true states.

## Contribution

It proposes a novel privacy-preserving method using output masks that are local and time-varying, ensuring privacy while maintaining system stability and convergence.

## Key findings

- Masked system converges to the same equilibrium as the original system.
- Existence of equilibrium points in masked systems conflicts with privacy preservation.
- Application demonstrated on social opinion, consensus, and synchronization models.

## Abstract

In multiagent dynamical systems, privacy protection corresponds to avoid disclosing the initial states of the agents while accomplishing a distributed task. The system-theoretic framework described in this paper for this scope, denoted dynamical privacy, relies on introducing output maps which act as masks, rendering the internal states of an agent indiscernible by the other agents as well as by external agents monitoring all communications. Our output masks are local (i.e., decided independently by each agent), time-varying functions asymptotically converging to the true states. The resulting masked system is also time-varying, and has the original unmasked system as its limit system. When the unmasked system has a globally exponentially stable equilibrium point, it is shown in the paper that the masked system has the same point as a global attractor. It is also shown that existence of equilibrium points in the masked system is not compatible with dynamical privacy. Application of dynamical privacy to popular examples of multiagent dynamics, such as models of social opinions, average consensus and synchronization, is investigated in detail.