The issue of privacy leakage in distributed consensus has garnered significant attention over the years, but existing studies often overlook the challenges posed by limited communication in algorithm design. This paper addresses the issue of privacy preservation in distributed weighted average consensus under limited communication scenarios. Specifically targeting directed and unbalanced topologies, we propose a privacy-preserving implementation protocol that incorporates the Paillier homomorphic encryption scheme. The protocol encrypts only the 1-bit quantized messages exchanged between agents, thus ensuring both the correctness of the consensus result and the confidentiality of each agent’s initial state. To demonstrate the practicality of the proposed method, we carry out numerical simulations that illustrate its ability to reach consensus effectively while ensuring the protection of private information.

This paper presents a novel finite-and-quantized output feedback asymptotic tracking control method for a general class of continuous-time linear time-invariant systems. First, we construct a finite quantizer with time-varying thresholds and design a pole placement control law that exclusively utilizes the finite-and-quantized output signal and an external reference signal. Then, we establish the boundedness of all closed-loop signals and prove the asymptotic convergence of the output tracking error to zero. The proposed method combines the advantages of classical pole placement control technique and finite quantization feedback technique. It not only reduces the requirement for feedback information compared with existing tracking control methods but also effectively handles unstable poles and zeros in controlled systems, thereby achieving asymptotic output tracking. Finally, we provide a representative example to validate the effectiveness and new features of our proposed method.