arXiv subjects

Xiaoxu Lyu

Publications and source records attributed to Xiaoxu Lyu.

7 recordsLinked to original sources

arXiv2026

Data-Driven Co-Design of Event-Triggered and Sparse Control for Resource-Aware Networked Control Systems

This paper investigates the data-driven co-design of event-triggered control (ETC) and sparse control (SC) for networked control systems (NCSs) with unknown linear dynamics. While ETC and SC have been widely studied as effective strategies to reduce communication and computation burdens on different resource dimensions, existing works typically address them separately and rely on accurate system models. Furthermore, their joint design in a data-driven setting, especially in the presence of measurement and process noise, remains largely unexplored. To bridge these gaps, we propose a unified data-driven framework that simultaneously accounts for bounded state and input measurement noise as well as process noise, and enables the co-design of ETC mechanisms and sparse controllers directly from data. Within this framework, we characterize stability, uniformly ultimately bounded (UUB) behavior, and $H_\infty$ performance under different noise conditions. For each problem, given the event-triggered parameters, we provide a sufficient condition for the existence of a feasible controller and develop an iterative algorithm to solve the associated nonconvex optimization problem. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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arXiv2026

Distributed State Estimation for Discrete-Time Linear Systems over Directed Graphs: A Measurement Perspective

This paper proposes a novel consensus-based distributed filter over directed graphs under the collectively observability condition. The distributed filter is designed using an augmented leader-following information fusion strategy, and the gain parameter is determined exclusively using local information. Additionally, the lower bound of the fusion step number is derived to ensure that the estimation error covariance remains uniformly upper-bounded. Furthermore, the lower bounds for the convergence rates of the steady-state performance gap between the proposed filter and the centralized filter are provided as the fusion step number approaches infinity. The analysis demonstrates that the convergence rate is at least as fast as exponential convergence, provided the communication topology satisfies the spectral norm condition. Finally, the theoretical results are validated through two simulation examples.

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arXiv2026

Data-Driven Structured Controller Design Using the Matrix S-Procedure

This paper focuses on the data-driven optimal structured controller design for discrete-time linear time-invariant (LTI) systems, considering both the $H_2$ performance and the $H_\infty$ performance. Specifically, we consider three scenarios: (i) the model-based structured control, (ii) the data-driven unstructured control, and (iii) the data-driven structured control. For the $H_2$ performance, we primarily investigate cases (ii) and (iii), since case (i) has been extensively studied in the literature. For the $H_\infty$ performance, all three scenarios are considered. For the structured control, we introduce a linearization technique that transforms the original nonconvex problem into a semidefinite programming (SDP) problem. Based on this transformation, we develop an iterative linear matrix inequality (ILMI) algorithm. For the data-driven control, we describe the set of all possible system matrices that can generate the sequence of collected data. Additionally, we propose a sufficient condition to handle all possible system matrices using the matrix S-procedure. The data-driven structured control is followed by combining the previous two cases. We compare our methods with those in the existing literature and demonstrate our superiority via several numerical simulations.

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arXiv2026

Bias-VarianceTrade-off in Kalman Filter-Based Disturbance Observers

The performance of disturbance observers is strongly influenced by the level of prior knowledge about the disturbance model. The simultaneous input and state estimation (SISE) algorithm is widely recognized for providing unbiased minimum-variance estimates under arbitrary disturbance models. In contrast, the Kalman filter-based disturbance observer (KF-DOB) achieves minimum mean-square error estimation when the disturbance model is fully specified. However, practical scenarios often fall between these extremes, where only partial knowledge of the disturbance model is available. This paper investigates the inherent bias-variance trade-off in KF-DOB when the disturbance model is incomplete. We further show that SISE can be interpreted as a special case of KF-DOB, where the disturbance noise covariance tends to infinity. To address this trade-off, we propose two novel estimators: the multi-kernel correntropy Kalman filter-based disturbance observer (MKCKF-DOB) and the interacting multiple models Kalman filter-based disturbance observer (IMMKF-DOB). Simulations verify the effectiveness of the proposed methods.

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arXiv2025

An Autocovariance Least-Squares-Based Data-Driven Kalman Filter for Unknown Systems

This article investigates the problem of data-driven state estimation for linear systems with both unknown system dynamics and noise covariances. We propose an Autocovariance Least-squares-based Data-driven Kalman Filter (ADKF), which provides a unified framework for simultaneous system identification and state estimation by utilizing pre-collected input-output trajectories and estimated initial states. Specifically, we design a SDP-based algorithm for estimating the noise covariances. We quantify the impact of model inaccuracy on noise covariances estimation using this identification algorithm, and introduce a feedback control mechanism for data collection to enhance the accuracy and stability of noise covariance estimation. The estimated noise covariances account for model inaccuracy, which are shown to be more suitable for state estimation. We also quantify the performance gap between the ADKF and the traditional Kalman filter with known system dynamics and noise covariances, showing that this gap decreases as the number and length of pre-collected trajectories increase. Finally, numerical simulations validate the robustness and effectiveness of the proposed ADKF.

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arXiv2025

On the Effects of Modeling Errors on Distributed Continuous-time Filtering

This paper offers a comprehensive performance analysis of the distributed continuous-time filtering in the presence of modeling errors. First, we introduce two performance indices, namely the nominal performance index and the estimation error covariance. By leveraging the nominal performance index and the Frobenius norm of the modeling deviations, we derive the bounds of the estimation error covariance and the lower bound of the nominal performance index. Specifically, we reveal the effect of the consensus parameter on both bounds. We demonstrate that, under specific conditions, an incorrect process noise covariance can lead to the divergence of the estimation error covariance. Moreover, we investigate the properties of the eigenvalues of the error dynamical matrix. Furthermore, we explore the magnitude relations between the nominal performance index and the estimation error covariance. Finally, we present some numerical simulations to validate the effectiveness of the theoretical results.

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arXiv2024

Performance Analysis of Distributed Filtering under Mismatched Noise Covariances

This paper systematically investigates the performance of consensus-based distributed filtering under mismatched noise covariances. First, we introduce three performance evaluation indices for such filtering problems,namely the standard performance evaluation index, the nominal performance evaluation index, and the estimation error covariance. We derive difference expressions among these indices and establish one-step relations among them under various mismatched noise covariance scenarios. We particularly reveal the effect of the consensus fusion on these relations. Furthermore, the recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these indices under the collective observability condition, and show this convergence condition of the nominal performance evaluation index can guarantee the convergence of the estimation error covariance. Additionally, we prove that the estimation error covariance of the consensus-based distributed filter under mismatched noise covariances can be bounded by the Frobenius norms of the noise covariance deviations and the trace of the nominal performance evaluation index. Finally, the effectiveness of the theoretical results is verified by numerical simulations.

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