Multi-agent systems (MASs) in open networks face dual security threats: Byzantine attacks that steer malicious consensus and eavesdroppers that steal private information. Existing resilient consensus protocol isolates Byzantine attacks by relying on (2f+1)-robust networks, which imposes stringent topological constraints and fails to provide privacy preservation simultaneously. To address this issue, an improved resilient consensus protocol withf(IRCP-f) is proposed, via absolute values of relative states, to defend againstf-local Byzantine attacks. This protocol only requires that an undirected and connected graph is (f+ 1)-robust instead of (2f+ 1)-robust. The properties of the dynamic network processed by the IRCP-fare analyzed, and the graph conditions for achieving average consensus are consequently satisfied. A fully distributed differentially private event-triggered average consensus (DPETAC) control scheme is then developed. With the DPETAC control scheme, convergence analysis, Zeno behavior analysis, accuracy analysis and privacy analysis are presented for the MAS. Finally, a numerical simulation illustrates the feasibility and effectiveness of the proposed privacy-preserving average consensus control scheme.

This article presents a linear active disturbance rejection control (LADRC) scheme for two-mass systems (TMSs) based on a singular perturbation (SP) approach. In the proposed scheme, the dynamics of TMSs are separated into a quasi-steady-state system at a slow time scale and a boundary-layer system at a fast time scale via the SP method. The quasi-steady-state model is used as the nominal model to design the LADRC, where internal model control (IMC) rules are employed for prescribed tracking performance. This not only reduces the model order but also makes the gain tuning straightforward, which is crucial for practical use. Based on the boundary-layer model, the active damping method is designed for vibration suppression, which aims at achieving a higher stable bandwidth of the IMC to better attenuate the residual disturbance of linear extended state observer such that the tracking accuracy can be improved. Stability of the full system was analyzed via the extended Tikhonov's theorem. Comparative experiments were carried out to verify the effectiveness of the proposed scheme.