arXiv subjects

Ji-Feng Zhang

Publications and source records attributed to Ji-Feng Zhang.

At least 19 recordsLinked to original sources

arXiv2026

CKKS Cryptosystem-Based Secure Parameter Identification for Multi-Participant ARX Systems

This paper investigates parameter identification for multi-participant autoregressive systems with exogenous input (ARX systems) while protecting the system input and output. A novel Cheon-Kim-Kim-Song (CKKS) cryptosystem-based secure parameter identification algorithm is proposed. By combining a modified CKKS cryptosystem and a proxy re-encryption scheme, the algorithm enables the fusion center to perform homomorphic operations on the ciphertexts which are encrypted using different secret keys. A sufficient condition on the truncation value of the truncated discrete Gaussian noise is derived to ensure the indistinguishability under chosen-plaintext attack (IND-CPA) security of the algorithm under collusion and quantum attacks. For convergence analysis, an auxiliary plaintext sequence is constructed to characterize the encryption noise and quantization error in the encrypted estimate. Using this sequence, a criterion for avoiding plaintext overflow is given, based on which the mean square convergence and convergence rate of the algorithm are given. A numerical example demonstrates the effectiveness and superior performance of the algorithm.

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arXiv2026

Privacy-Preserving Cramér-Rao Lower Bound

This paper establishes the privacy-preserving Cramer-Rao lower bound (CRLB) theory, characterizing the fundamental limit of identification accuracy under privacy constraint for general stochastic obfuscation mechanisms. An identifiability criterion under privacy constraint is derived by using Fisher information matrix as the privacy metric. In the identifiable case, a precise privacy-preserving CRLB is established with an explicit expression, which quantifies the privacy cost without unspecified constant factors. Considering computational efficiency, recursive formulas are developed to compute the privacy-preserving CRLB for multi-measurement systems, reducing the computational burden caused by direct high-dimensional matrix inversion. To demonstrate the tightness of the lower bound, a Gaussian-mechanism-based privacy-preserving RLS algorithm is shown to exactly attain the bound under Gaussian measurement noises, and a maximum-likelihood-based privacy-preserving identification algorithm is proposed to attain the bound in the sense of convergence rates under non-Gaussian measurement noises. For applicability, the proposed theory can be extended to dynamic model state estimation, distributed estimation, and average consensus. Experimental results are provided to demonstrate the privacy-preserving CRLB and show the effectiveness of the proposed algorithms.

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arXiv2026

Distributed recursive binary identification under tampering and non-persistent excitation

In this paper, we consider distributed parameter estimation with binary observations under measurement-side tampering: each node observes a thresholded output whose label may be flipped and exchanges information over a communication graph. We develop a distributed recursive projection algorithm based on the diffusion strategy. Without imposing independence, stationarity, or Gaussian assumptions, we establish almost sure upper bounds of both the accumulated regrets of the adaptive predictor and the distributed estimation error. Under a mild cooperative excitation condition, all nodes' estimate are consistent, even when each node is individually non-exciting. Simulations on a jointly exciting network corroborate the theory and show that the proposed algorithm converges, whereas non-cooperative and tampering-unaware baselines do not.

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arXiv2026

Differentially Private Consensus for Time-Delay Multi-agent Systems

This paper is concerned with the differentially private consensus problem for discrete-time multi-agent systems with communication delays. The purpose of the paper is to achieve differentially private consensus for such systems while protecting the entire delayed initial histories of all agents. A novel adjacency relation for delayed histories is introduced, and a Laplace-noise-based privacy mechanism is developed, where the noise variance is allowed to vary with time and even increase. By using the difference resolvent function method, decay estimates for the fundamental solutions of the delayed difference equations are derived. Based on these estimates and a backstepping technique, mean square weak consensus, mean square strong consensus, and almost sure strong consensus are established. The estimates for the fundamental solutions are also used to derive an explicit sensitivity bound. Furthermore, a constructive parameter design is provided to achieve a prescribed infinite-horizon $ε^\star$-differential privacy level. Numerical simulations illustrate the theoretical results.

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arXiv2026

Distributed Fusion Estimation with Protecting Exogenous Inputs

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.

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arXiv2026

Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs

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".

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arXiv2026

Closed-loop solvability of delayed control problems: A stochastic Volterra system approach

A general and new stochastic linear quadratic optimal control problem is studied, where the coefficients are allowed to be time-varying, and both state delay and control delay can appear simultaneously in the state equation and the cost functional. The closed-loop outcome control of this delayed problem is given by a new Riccati system whose solvability is carefully established. To this end, a novel method is introduced to transform the delayed problem into a control problem driven by a stochastic Volterra integral system without delay. This method offers several advantages: it bypasses the difficulty of decoupling the forward delayed state equation and the backward anticipated adjoint equation, avoids the introduction of infinite-dimensional spaces and unbounded control operators, and ensures that the closed-loop outcome control depends only on past state and control, without relying on future state or complex conditional expectation calculations. Finally, several particular important stochastic systems are discussed. It is found that the model can cover a class of stochastic integro-differential systems, whose closed-loop solvability has not been available before.

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arXiv2026

Privacy-Preserving Distributed Estimation with Limited Data Rate

This paper focuses on the privacy-preserving distributed estimation problem with a limited data rate, where the observations are the sensitive information. Specifically, a binary-valued quantizer-based privacy-preserving distributed estimation algorithm is developed, which improves the algorithm's privacy-preserving capability and simultaneously reduces the communication costs. The algorithm's privacy-preserving capability, measured by the Fisher information matrix, is dynamically enhanced over time. Notably, the Fisher information matrix of the output signals with respect to the sensitive information converges to zero at a polynomial rate, and the improvement in privacy brought by the quantizers is quantitatively characterized as a multiplicative effect. Regarding the communication costs, each sensor transmits only 1 bit of information to its neighbours at each time step. Additionally, the assumption on the negligible quantization error for real-valued messages is not required. While achieving the requirements of privacy preservation and reducing communication costs, the algorithm ensures that its estimates converge almost surely to the true value of the unknown parameter by establishing a co-design guideline for the time-varying privacy noises and step-sizes. A polynomial almost sure convergence rate is obtained, and then the trade-off between privacy and convergence rate is established. Numerical examples demonstrate the main results.

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arXiv2025

Observer-based Differentially Private Consensus for Linear Multi-agent Systems

This paper investigates the differentially private consensus problem for general linear multi-agent systems (MASs) based on output feedback protocols. To protect the output information, which is considered private data and may be at high risk of exposure, Laplace noise is added to the information exchange. The conditions for achieving mean square and almost sure consensus in observer-based MASs are established using the backstepping method and the convergence theory for nonnegative almost supermartingales. It is shown that the separation principle remains valid for the consensus problem of linear MASs with decaying Laplace noise. Furthermore, the convergence rate is provided. Then, a joint design framework is developed for state estimation gain, feedback control gain, and noise to ensure the preservation of ε-differential privacy. The output information of each agent is shown to be protected at every time step. Finally, sufficient conditions are established for simultaneously achieving consensus and preserving differential privacy for linear MASs utilizing both full-order and reduced-order observers. Meanwhile, an ε*-differentially private consensus is achieved to meet the desired privacy level. Two simulation examples are provided to validate the theoretical results.

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arXiv2025

Leader-Follower Mean Field LQG Games with Multiplicative Noise

This paper studies open-loop and feedback solutions to leader-follower mean field linear-quadratic-Gaussian games with multiplicative noise by the direct approach. The leader-follower game involves a leader and many followers, where the state and control weight matrices in their costs are not limited to be positive definite. From variational analysis with mean field approximations, we obtain a set of open-loop controls in terms of solutions to mean field forward-backward stochastic differential equations. By applying the matrix maximum principle, a set of decentralized feedback strategies is constructed. Distinct from traditional works, a cross term has appeared in derivation due to the presence of mean field terms. For open-loop and feedback solutions, the corresponding optimal costs of all players are explicitly given in terms of the solutions to two Riccati equations, respectively.

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arXiv2025

Quantized Distributed Estimation with Event-triggered Communication and Packet Loss

This paper focuses on the problem of quantized distributed estimation with event-triggered communication and packet loss, aiming to reduce the number of transmitted bits. The main challenge lies in the inability to differentiate between an untriggered event and a packet loss occurrence. This paper proposes an event-triggered distributed estimation algorithm with quantized communication and quantized measurement, in which it introduces a one-bit information reconstruction method to deal with packet loss. The almost sure convergence and convergence rate of the proposed algorithm are established. Besides, it is demonstrated that the global average communication bit-rate decreases to zero over time. Moreover, the trade-off between communication rate and convergence rate is revealed, providing guidance for designing the communication rate required to achieve the algorithm's convergence rate. A numerical example is supplied to validate the findings.

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arXiv2025

Recursive Binary Identification under Data Tampering and Non-Persistent Excitation with Application to Emission Control

This paper studies the problem of online parameter estimation for cyber-physical systems with binary outputs that may be subject to adversarial data tampering. Existing methods are primarily offline and unsuitable for real-time learning. To address this issue, we first develop a first-order gradient-based algorithm that updates parameter estimates recursively using incoming data. Considering that persistent excitation (PE) conditions are difficult to satisfy in feedback control scenarios, a second-order quasi-Newton algorithm is proposed to achieve faster convergence without requiring the PE condition. For both algorithms, corresponding versions are developed to handle known and unknown tampering strategies, and their parameter estimates are proven to converge almost surely over time. In particular, the second-order algorithm ensures convergence under a signal condition that matches the minimal excitation required by classical least-squares estimation in stochastic regression models. The second-order algorithm is also extended to an adaptive control framework, providing an explicit upper bound on the tracking error for binary-output FIR systems under unknown tampering. Three numerical simulations verify the theoretical results and show that the proposed methods are robust against data tampering. Finally, the approach is validated via a vehicle emission control problem, where it effectively improves the detection accuracy of excess-emission events.

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arXiv2025

State Estimation with Protecting Exogenous Inputs via Cramér-Rao Lower Bound Approach

This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cramér-Rao lower bound (CRLB) is employed to constrain the mean square error (MSE) of the adversary's estimate for the exogenous inputs above a specified threshold. By minimizing the MSE of the state estimate while ensuring a certain privacy level measured by CRLB, the problem is formulated as a constrained optimization. To solve the optimization problem, an explicit expression for CRLB is first provided. As the computational complexity of the CRLB increases with the time step, a low-complexity approach is proposed to make the complexity independent of time. Then, a relaxation approach is proposed to efficiently solve the optimization problem. Finally, a privacy-preserving state estimation algorithm with low complexity is developed, which also ensures $(ε, δ)$-differential privacy. Two illustrative examples, including a practical scenario for protecting building occupancy, demonstrate the effectiveness of the proposed algorithm.

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arXiv2025

Differentially Private Distributed Nonconvex Stochastic Optimization with Quantized Communication

This paper proposes a new distributed nonconvex stochastic optimization algorithm that can achieve privacy protection, communication efficiency and convergence simultaneously. Specifically, each node adds general privacy noises to its local state to avoid information leakage, and then quantizes its noise-perturbed state before transmitting to improve communication efficiency. By using a subsampling method controlled through the sample-size parameter, the proposed algorithm reduces cumulative differential privacy parameters ε, δ, and thus enhances the differential privacy level, which is significantly different from the existing works. By using a two-time-scale step-sizes method, the mean square convergence for nonconvex cost functions is given. Furthermore, when the global cost function satisfies the Polyak-Lojasiewicz condition, the convergence rate and the oracle complexity of the proposed algorithm are given. In addition, the proposed algorithm achieves both the mean square convergence and finite cumulative differential privacy parameters ε, δ over infinite iterations as the sample-size goes to infinity. A numerical example of the distributed training on the "MNIST" dataset is given to show the effectiveness of the algorithm.

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arXiv2025

Signal-Comparison-Based Distributed Estimation Under Decaying Average Data Rate Communications

The paper investigates the distributed estimation problem under low bit rate communications. Based on the signal-comparison (SC) consensus protocol under binary-valued communications, a new consensus+innovations type distributed estimation algorithm is proposed. Firstly, the high-dimensional estimates are compressed into binary-valued messages by using a periodic compressive strategy, dithered noises and a sign function. Next, based on the dithered noises and expanding triggering thresholds, a new stochastic event-triggered mechanism is proposed to reduce the communication frequency. Then, a modified SC consensus protocol is applied to fuse the neighborhood information. Finally, a stochastic approximation estimation algorithm is used to process innovations. The proposed SC-based algorithm has the advantages of high effectiveness and low communication cost. For the effectiveness, the estimates of the SC-based algorithm converge to the true value in the almost sure and mean square sense. A polynomial almost sure convergence rate is also obtained. For the communication cost, the local and global average bit rates for communications decay to zero at a polynomial rate. The trade-off between the convergence rate and the communication cost is established through event-triggered coefficients. A better convergence rate can be achieved by decreasing event-triggered coefficients, while lower communication cost can be achieved by increasing event-triggered coefficients. A simulation example is given to demonstrate the theoretical results.

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arXiv2025

Recursive Identification of Binary-Valued Systems under Uniform Persistent Excitations

This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or truncations is proposed. The algorithm overcomes the limitations of the existing empirical measurement method and the recursive projection method, where the former requires periodic inputs, and the latter requires projections to restrict the search region in a compact set.To analyze the convergence property of the algorithm, the distribution tail of the estimation error is proved to be exponentially convergent through an auxiliary stochastic process. Based on this key technique, the SA-based algorithm appears to be the first to reach the almost sure convergence rate of $ O(\sqrt{\ln\ln k/k}) $ theoretically in the non-periodic input case. Meanwhile, the mean square convergence is proved to have a rate of $ O(1/k) $, which is the best one even under accurate observations. A numerical example is given to demonstrate the effectiveness of the proposed algorithm and theoretical results.

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arXiv2025

One-bit consensus of controllable linear multi-agent systems with communication noises

This paper addresses the one-bit consensus of controllable linear multi-agent systems (MASs) with communication noises. A consensus algorithm consisting of a communication protocol and a consensus controller is designed. The communication protocol introduces a linear compression encoding function to achieve a one-bit data rate, thereby saving communication costs. The consensus controller with a stabilization term and a consensus term is proposed to ensure the consensus of a potentially unstable but controllable MAS. Specifically, in the consensus term, we adopt an estimation method to overcome the information loss caused by one-bit communications and a decay step to attenuate the effect of communication noise. Two combined Lyapunov functions are constructed to overcome the difficulty arising from the coupling of the control and estimation. By establishing similar iterative structures of these two functions, this paper shows that the MAS can achieve consensus in the mean square sense at the rate of the reciprocal of the iteration number under the case with a connected fixed topology. Moreover, the theoretical results are generalized to the case with jointly connected Markovian switching topologies by establishing a certain equivalence relationship between the Markovian switching topologies and a fixed topology. Two simulation examples are given to validate the algorithm.

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arXiv2025

Differentially Private Recursive Least Squares Estimation for ARX Systems with Multi-Participants

This paper proposes a differentially private recursive least squares algorithm to estimate the parameter of autoregressive systems with exogenous inputs and multi-participants (MP-ARX systems) and protect each participant's sensitive information from potential attackers. We first give a rigorous differential privacy analysis of the algorithm, and establish the quantitative relationship between the added noises and the privacy-preserving level when the system is asymptotically stable. The asymptotic stability of the system is necessary for ensuring the differential privacy of the algorithm. We then give an estimation error analysis of the algorithm under the general and possible weakest excitation condition without requiring the boundedness, independence and stationarity on the regression vectors. Particularly, when there is no regression term in the system output and the differential privacy only on the system output is considered, $\varepsilon$-differential privacy and almost sure convergence of the algorithm can be established simultaneously. To minimize the estimation error of the algorithm with $\varepsilon$-differential privacy, the existence of the noise intensity is proved. Finally, two examples are given to show the efficiency of the algorithm.

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