Sampled-Data-Based Privacy-Preserving Scaled Consensus for Nonlinear Multiagent Systems: A Paillier Encryption Approach

This article is concerned with the privacy preservation problem for scaled consensus in nonlinear multiagent systems (MASs) through sampled data. In scaled consensus, the aim is for agents’ states to achieve specified proportions rather than converging to a single value, and this approach encompasses standard consensus, bipartite consensus, and cluster consensus within its framework. To prevent the leakage of sensitive data during communication, a novel privacy-preserving scaled distributed protocol is proposed. This protocol uses homomorphic encryption, whereby agents initially encrypt their information and transmit it in ciphertext form to neighboring agents. The control protocol is then reconstructed by the agents using the encrypted information received from their neighbors. A modified Halanay-like inequality is formulated and, by leveraging algebraic graph theory and the Lyapunov stability theorem, sufficient conditions are established to ensure that the MASs can achieve exponentially ultimately bounded scaled consensus. Furthermore, a convex optimization method is adopted to identify the optimal control gain so as to maximize the allowable sampling interval bound. The theoretical results are substantiated through a numerical simulation.