arXiv subjects

Dawei Shi

Publications and source records attributed to Dawei Shi.

At least 19 recordsLinked to original sources

arXiv2026

Hierarchical Variational Kalman Filtering

Traditional variational Kalman filtering with unknown noise statistics suffers from inconsistent process covariance estimation and slow convergence speed, limiting its practical utility. To address these issues, we introduce a surrogate variable representing the process-noise-free state, which enables explicit modeling and inference of process noise statistics. In addition, we reformulate the conventional coordinate ascent variation inference (CAVI) as a marginalized maximum a posteriori problem, followed by a single-step hyperparameter fitting. This reformulation obviates the need for multiple inner iterations inherent to CAVI and decouples the design of the covariance tracking filters. Consequently, this architecture permits the deployment of higher-order filters for covariance tracking and enables sliding-window hyperparameter estimation. Notably, when this window encompasses all historical data, the covariance tracking estimator intrinsically operates as a zero-phase filter. Numerical simulations validate the theoretical framework, demonstrating the enhanced convergence speed and superior estimation accuracy compared with existing methods.

stat.ML↗

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.

math.OC↗

arXiv2025

Variational Robust Kalman Filters: A Unified Framework

Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical applications, both process and measurement noise can be influenced by outliers, be time-varying, or both. In this work, we propose a variational robust Kalman filter, built on a Student's $t$-distribution induced loss function and variational inference, and solved in a computationally efficient manner. We demonstrate that robustness can be understood as a prerequisite for adaptivity, making it possible to merge the above two competing goals into a single framework through a probabilistic switching rule. Additionally, our proposed filter can recover conventional KF, robust KF, and adaptive KF by tuning parameters, and can suppress both the imperfect process and measurement noise, enabling it to perform superiorly in complex noise environments. Simulations verify the effectiveness of the proposed method.

cs.IT↗

arXiv2025

Event-triggered Dual Gradient Tracking for Distributed Resource Allocation

High communication costs create a major bottleneck for distributed resource allocation over unbalanced directed networks. Conventional dual gradient tracking methods, while effective for problems on unbalanced digraphs, rely on periodic communication that creates significant overhead in resource-constrained networks. This paper introduces a novel event-triggered dual gradient tracking algorithm to mitigate this limitation, wherein agents communicate only when local state deviations surpass a predefined threshold. We establish comprehensive convergence guarantees for this approach. First, we prove sublinear convergence for non-convex dual objectives and linear convergence under the Polyak-{\L}ojasiewicz condition. Building on this, we demonstrate that the proposed algorithm achieves sublinear convergence for general strongly convex cost functions and linear convergence for those that are also Lipschitz-smooth. Numerical experiments confirm that our event-triggered method significantly reduces communication events compared to periodic schemes while preserving comparable convergence performance.

eess.SY↗

arXiv2025

Improved Extended Kalman Filter-Based Disturbance Observers for Exoskeletons

The nominal performance of mechanical systems is often degraded by unknown disturbances. A two-degree-of-freedom control structure can decouple nominal performance from disturbance rejection. However, perfect disturbance rejection is unattainable when the disturbance dynamic is unknown. In this work, we reveal an inherent trade-off in disturbance estimation subject to tracking speed and tracking uncertainty. Then, we propose two novel methods to enhance disturbance estimation: an interacting multiple model extended Kalman filter-based disturbance observer and a multi-kernel correntropy extended Kalman filter-based disturbance observer. Experiments on an exoskeleton verify that the proposed two methods improve the tracking accuracy $36.3\%$ and $16.2\%$ in hip joint error, and $46.3\%$ and $24.4\%$ in knee joint error, respectively, compared to the extended Kalman filter-based disturbance observer, in a time-varying interaction force scenario, demonstrating the superiority of the proposed method.

cs.RO↗

arXiv2025

Online Coreset Selection for Learning Dynamic Systems

With the increasing availability of streaming data in dynamic systems, a critical challenge in data-driven modeling for control is how to efficiently select informative data to characterize system dynamics. In this work, we develop an online coreset selection method for set-membership identification in the presence of process disturbances, improving data efficiency while preserving convergence guarantees. Specifically, we derive a stacked polyhedral representation that over-approximates the feasible parameter set. Based on this representation, we propose a geometric selection criterion that retains a data point only if it induces a sufficient contraction of the feasible set. Theoretically, the feasible-set volume is shown to converge to zero almost surely under persistently exciting data and a tight disturbance bound. When the disturbance bound is mismatched, an explicit Hausdorff-distance bound is derived to quantify the resulting identification error. In addition, an upper bound on the expected coreset size is established and extensions to nonlinear systems with linear-in-the-parameter structures and to bounded measurement noise are discussed. The effectiveness of the proposed method is demonstrated through comprehensive simulation studies.

eess.SY↗

arXiv2025

Thompson Sampling-Based Learning and Control for Unknown Dynamic Systems

Thompson sampling (TS) is a Bayesian randomized exploration strategy that samples options (e.g., system parameters or control laws) from the current posterior and then applies the selected option that is optimal for a task, thereby balancing exploration and exploitation; this makes TS effective for active learning-based controller design. However, TS relies on finite parametric representations, which limits its applicability to more general spaces, which are more commonly encountered in control system design. To address this issue, this work proposes a parameterization method for control law learning using reproducing kernel Hilbert spaces and designs a data-driven active learning control approach. Specifically, the proposed method treats the control law as an element in a function space, allowing the design of control laws without imposing restrictions on the system structure or the form of the controller. A TS framework is proposed in this work to reduce control costs through online exploration and exploitation, and the convergence guarantees are further provided for the learning process. Theoretical analysis shows that the proposed method learns the relationship between control laws and closed-loop performance metrics at an exponential rate, and the upper bound of control regret is also derived. Furthermore, the closed-loop stability of the proposed learning framework is analyzed. Numerical experiments on controlling unknown nonlinear systems validate the effectiveness of the proposed method.

cs.LG↗

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.

eess.SY↗

arXiv2025

Quantum Direct Steganography Scheme Based on Modified Generator Projection Directions of Steane Code over a Single-Type Pauli Channel

In quantum mechanics, measurements of a quantum state in various directions yield distinct outcomes, a principle that forms the foundation of quantum communication theory. This paper expands upon this concept by introducing a method to modify generator projection directions (MGPD) within quantum stabilizer codes. Employing the Steane code ($(7,1,3)$ code), as a fundamental carrier, we develop a novel scheme for direct quantum steganography across a single-type Pauli channel. The infeasibility of eavesdropping decoding under MGPD is proven. We detail the steganographic encoding and decoding schemes, corresponding quantum circuits, and eavesdropping detection principles. We also use a 'Sudoku'-style strategy to balance steganographic error probabilities and provide the complete steganography protocol. Relative to existing studies, the MGPD method achieves embedding rates approaching and attaining the upper limit of the information capacity for the $(n,k,d)=(7,1,3)$ code within a noise probability range of approximately $1/(n+1)=12.5\%$. It also reduces the consumption of auxiliary keys from $O(\log{(N)})$ to $O(1)$, while enabling eavesdropping detection and steganography of arbitrary quantum states. We investigate its potential applications in quantum communication and assess its benefits in the context of secret information transmission and eavesdropping detection in noisy channels. Although the MGPD method incorporates certain idealized assumptions and limitations, it provides novel perspectives on the concealment of quantum information.

quant-ph↗

arXiv2024

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.

eess.SP↗

arXiv2024

Open-/Closed-loop Active Learning for Data-driven Predictive Control

An important question in data-driven control is how to obtain an informative dataset. In this work, we consider the problem of effective data acquisition of an unknown linear system with bounded disturbance for both open-loop and closed-loop stages. The learning objective is to minimize the volume of the set of admissible systems. First, a performance measure based on historical data and the input sequence is introduced to characterize the upper bound of the volume of the set of admissible systems. On the basis of this performance measure, an open-loop active learning strategy is proposed to minimize the volume by actively designing inputs during the open-loop stage. For the closed-loop stage, a closed-loop active learning strategy is designed to select and learn from informative closed-loop data. The efficiency of the proposed closed-loop active learning strategy is proved by showing that the unselected data cannot benefit the learning performance. Furthermore, an adaptive predictive controller is designed in accordance with the proposed data acquisition approach. The recursive feasibility and the stability of the controller are proved by analyzing the effect of the closed-loop active learning strategy. Finally, numerical examples and comparisons illustrate the effectiveness of the proposed data acquisition strategy.

eess.SY↗

arXiv2024

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.

eess.SY↗

arXiv2024

Information-triggered Learning with Application to Learning-based Predictive Control

Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the abundance of data becomes overwhelming. To address this issue, this work proposes an information-triggered learning framework and a corresponding learning-based controller design approach with guaranteed stability. Specifically, we consider a linear time-invariant system with unknown dynamics. A set-membership approach is introduced to learn a parametric uncertainty set for the unknown dynamics. Then, a data selection mechanism is proposed by evaluating the incremental information in a data sample, where the incremental information is quantified by its effects on shrinking the parametric uncertainty set. Next, after introducing a stability criterion using the set-membership estimate of the system dynamics, a robust learning-based predictive controller (LPC) is designed by minimizing a worst-case cost function. The closed-loop stability of the LPC equipped with the information-triggered learning protocol is discussed within a high-probability framework. Finally, comparative numerical experiments are performed to verify the validity of the proposed approach.

eess.SY↗

arXiv2023

Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation

Disturbance observers have been attracting continuing research efforts and are widely used in many applications. Among them, the Kalman filter-based disturbance observer is an attractive one since it estimates both the state and the disturbance simultaneously, and is optimal for a linear system with Gaussian noises. Unfortunately, The noise in the disturbance channel typically exhibits a heavy-tailed distribution because the nominal disturbance dynamics usually do not align with the practical ones. To handle this issue, we propose a generalized multi-kernel maximum correntropy Kalman filter for disturbance estimation, which is less conservative by adopting different kernel bandwidths for different channels and exhibits excellent performance both with and without external disturbance. The convergence of the fixed point iteration and the complexity of the proposed algorithm are given. Simulations on a robotic manipulator reveal that the proposed algorithm is very efficient in disturbance estimation with moderate algorithm complexity.

eess.SY↗

arXiv2023

Multi-kernel Correntropy Regression: Robustness, Optimality, and Application on Magnetometer Calibration

This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal that the kernel bandwidth should be neither too small nor too big in the sense of the lowest upper error bound. Meanwhile, we find that the proposed MKC is related to a specific heavy-tail distribution, and the level of the heavy tail is controlled by the kernel bandwidth solely. Interestingly, this distribution becomes the Gaussian distribution when the bandwidth is set to be infinite, which allows one to tackle both Gaussian and non-Gaussian problems. We propose an expectation-maximization (EM) algorithm to estimate the parameter vectors and explore the kernel bandwidths alternatively. The results show that our algorithm is equivalent to the traditional linear regression under Gaussian noise and outperforms the conventional method under heavy-tailed noise. Both numerical simulations and experiments on a magnetometer calibration application verify the effectiveness of the proposed method.

eess.SY↗

arXiv2023

Multi-kernel Correntropy-based Orientation Estimation of IMUs: Gradient Descent Methods

This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors.

eess.SY↗

arXiv2022

Event-triggered Observability: A Set-membership Perspective

This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $\epsilon$-observability is defined with parameter $\epsilon$, which relates to the worst-case performance of inferring the initial state based on not only the received measurement but also the implicit information in the event-triggering conditions at no-event instants. A criterion is developed to test the proposed $\epsilon$-observability of discrete-time linear systems, based on which an iterative event-triggered set-membership observer is designed to evaluate a set containing all possible values of the state. The proposed set-membership observer is designed as the outer approximation of the ellipsoids predicted based on previous state estimates and the ellipsoids inferred by fusing the received measurement and communication conditions, which is optimal in the sense of trace at each step and is proved to be asymptotically bounded. The efficiency of the proposed event-triggered set-membership state observer is verified by numerical experiments.

eess.SY↗

arXiv2021

Quasi Time-Fuel Optimal Control Strategy for dynamic target tracking

This brief proposes a quasi time-fuel optimal control strategy to solve the dynamic tracking problem of unmanned systems when fuel and control input are limited. This kind of motion planning and control strategy could bring the biggest advantage into full play in the field of switching tracking for multiple targets, such as the multi-target strike of weapons and the rapid multi-target grabbing of robots on industrial assembly lines. Compared with the time-fuel optimal control that has been studied before, the proposed controller retains the advantages of optimal control when switching between multiple dynamic targets, and improves the high-frequency oscillation problem of the system under the discontinuous control strategy. Moreover, the asymmetry of friction load, which can affect the dynamic performance of the system, is also considered in this brief. Therefore, the novel control law, which is addressed by this brief, can make the corresponding system achieve the desired transient performance and satisfactory steady-state performance when switching between multiple dynamic targets. The experiment results based on the visual tracking turntable are presented to verify the superiority of the proposed method.

physics.pop-ph↗