Privacy preserving synchronization of directed dynamical networks with periodic data-sampling

Data privacy has become a key issue in networked systems, but few effort was devoted to privacy preservation in synchronization of nonlinear dynamical networks when data sampling is involved. This work focuses on the privacy preserving synchronization in a type of nonlinear dynamical network with sampled data. In order to preserve their private initial states, the nodes conceal the sampled data via certain deterministic perturbation, and exchange the masked data with their neighbors via the communication network. A novel privacy-preserving protocols with sampled data is developed, which differs from existing designs with continuous data, and a commonly used restriction on the nodes’ neighbor sets is unnecessary herein. By establishing a new Halanay-type inequality with decaying perturbation, some sufficient criteria are derived to guarantee synchronization without disclosing the nodes’ privacy, revealing how the decaying rate of the masking functions, the topology and the sampling period influence synchronization. Furthermore, in order to reduce the control update, the analogue of the above design with event-trigger is also given, leading to another useful condition for privacy preserving synchronization. Some numerical examples are finally given to validate the theoretical results and demonstrate the effectiveness of the proposed designs.