Ji-Feng Zhang

Xiaofeng Zong, Tao Li, Ji-Feng Zhang

This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations. By the martingale convergence theorem, we obtain necessary conditions and sufficient conditions for stochastic strong consensus. For the case of multiplicative noises, we consider two kinds of time-delays, appeared in the measurement term and the noise term, respectively. We first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus. Then by constructing degenerate Lyapunov functional, we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time-delay in the measurement term.

Liping Guo, Jimin Wang, Yanlong Zhao et al.

In the context of distributed fusion estimation, directly transmitting local estimates to the fusion center may cause a privacy leakage concerning exogenous inputs. Thus, it is crucial to protect exogenous inputs against full eavesdropping while achieving distributed fusion estimation. To address this issue, a noise injection strategy is provided by injecting mutually independent noises into the local estimates transmitted to the fusion center. To determine the covariance matrices of the injected noises, a constrained minimization problem is constructed by minimizing the sum of mean square errors of the local estimates while ensuring (ε, δ)-differential privacy. Suffering from the non-convexity of the minimization problem, an approach of relaxation is proposed, which efficiently solves the minimization problem without sacrificing differential privacy level. Then, a differentially private distributed fusion estimation algorithm based on the covariance intersection approach is developed. Further, by introducing a feedback mechanism, the fusion estimation accuracy is enhanced on the premise of the same (ε, δ)-differential privacy. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed algorithms, and the trade-off between differential privacy level and fusion estimation accuracy.

Yang Meng, Tao Li, Ji-Feng Zhang

In this note, the coordination of linear discrete-time multi-agent systems over digital networks is investigated with unmeasurable states in agents' dynamics. The quantized-observer based communication protocols and Certainty Equivalence principle based control protocols are proposed to characterize the inter-agent communication and the cooperative control in an integrative framework. By investigating the structural and asymptotic properties of the equations of stabilization and estimation errors nonlinearly coupled by the finite-level quantization scheme, some necessary conditions and sufficient conditions are given for the existence of such communication and control protocols to ensure the inter-agent state observation and cooperative stabilization. It is shown that these conditions come down to the simultaneous stabilizability and the detectability of the dynamics of agents and the structure of the communication network.

Jialong Chen, Ji-Feng Zhang

This paper investigates the parameter identification for multi-participant autoregressive exogenous input (ARX) systems while protecting the system input and output. To do so, the discrete Gaussian noise in the standard Cheon-Kim-Kim-Song (CKKS) cryptosystem is replaced with a truncated one. By using the CKKS cryptosystem with the truncated discrete Gaussian noise and the key-switching technique, a proxy re-encryption scheme is developed. Based on this scheme, a secure parameter identification algorithm is proposed for multi-participant ARX systems. By rigorously proving that the statistical distance between the discrete Gaussian noise and the truncated one is negligible, the polynomial-time reduction between the standard Ring-Learning with Errors (RLWE) problem and the RLWE problem with the truncated discrete Gaussian noise is established. This result ensures the indistinguishability under chosen-plaintext attacks (IND-CPA) security of the algorithm. By giving a lower bound condition on the size of the plaintext space, the computational overflow in encryption is avoided. Based on this condition, the mean square convergence and convergence rate of the algorithm are given. The trade-off between the security level and the convergence of the algorithm is presented. Finally, a numerical example is given to verify the effectiveness of the algorithm.

Jialong Chen, Jimin Wang, Ji-Feng Zhang

This paper proposes a differentially private gradient-tracking-based distributed stochastic optimization algorithm over directed graphs. In particular, privacy noises are incorporated into each agent's state and tracking variable to mitigate information leakage, after which the perturbed states and tracking variables are transmitted to neighbors. We design two novel schemes for the step-sizes and the sampling number within the algorithm. The sampling parameter-controlled subsampling method employed by both schemes enhances the differential privacy level, and ensures a finite cumulative privacy budget even over infinite iterations. The algorithm achieves both almost sure and mean square convergence for nonconvex objectives. Furthermore, when nonconvex objectives satisfy the Polyak-Lojasiewicz condition, Scheme (S1) achieves a polynomial mean square convergence rate, and Scheme (S2) achieves an exponential mean square convergence rate. The trade-off between privacy and convergence is presented. The effectiveness of the algorithm and its superior performance compared to existing works are illustrated through numerical examples of distributed training on the benchmark datasets "MNIST" and "CIFAR-10".