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

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.Comment: 38 pages, 4 figures, extended version of arXiv preprint arXiv:1808.0808

On the stability of the Kuramoto model of coupled nonlinear oscillators

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.Comment: 8 Pages. An earlier version appeared in the proceedings of the American Control Conference, Boston, MA, June 200