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IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)

作者： Yu, Xian Ji, Xiaoqiang Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Guangdong Peoples R China Chinese Univ Hong Kong Shenzhen Inst Artificial Intelligence & Robot Soc Shenzhen 518172 Guangdong Peoples R China Chinese Univ Hong Kong Sch Sci & Engn Shenzhen 518172 Guangdong Peoples R China

ISBN: (纸本)9798350321050

An important task in the identification community for time-varying systems is to track the possible changes in system dynamics as well as possible. For the currently applied identification techniques, this task is usually implemented at the cost of increasing the computational quantity as the time increases, or of adding a forgetting factor that requires to be determined a priori. In this paper we develop an estimation approach for linear time-varying systems with additive disturbances, which achieves a major computational advantage without determining the additional factor. In particular, we integrate the idea behind Savitaky-Golay filtering into the kernel-based regularization method under the framework of regularized least squares. It is found that the developed approach remains the same computational quantity during the whole time interval in the estimating procedure. A numerical example is simulated to validate the effectiveness of the developed approach.

关键词： System Identification Linear Time-varying System Savitaky-Golay Filtering kernel-based regularization method

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kernel-based regularization least squares algorithm for nonlinear time-delayed systems using self-organizing maps

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2023年第8期33卷 4602-4615页

作者： Zhang, Zili Zhang, Yanxin Chen, Jing Guo, Liuxiao Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China

This article proposes a kernel-based regularization least squares algorithm for nonlinear time-delayed systems with unknown structure. Since the structure and the time-delay of the model are unknown, a model pool constituted of several Volterra series is constructed with the aim of approximating the nonlinear model which has different time-delays. Then, a self-organizing maps method and a kernel-based regularization method are interactively used to update the time-delay and parameters. Compared with the traditional algorithms, the proposed algorithm has no limitation on the nonlinear model, and can describe the dynamics of the nonlinear model with a simple structure. Finally, simulation examples are given to show the effectiveness of the algorithm.

关键词： kernel-based regularization method least squares algorithm nonlinear time-delayed systems self-organizing maps Volterra series

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Clustering of Linear Time-Invariant Systems: A Bayesian Nonparametric method

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IFAC-PapersOnLine 2023年第2期56卷 10527-10532页

作者： Xiaoquan Tang Tianshi Chen

In this paper, we consider the clustering of linear time-invariant (LTI) systems according to the similarity of dynamics. There are two main difficulties for clustering of LTI systems: one is to determine the labels of LTI systems and the number of clusters, and another one is to build models of LTI systems. To address these two difficulties simultaneously, a Bayesian nonparametric method based on Dirichlet process mixture models (DPMM) and kernel-based regularization method is proposed. To be specific, the Dirichlet process mixtures of Bayesian linear regression models (DPM-BLRM) is proposed to determine the label of each LTI system according to the probability that the system belongs to each cluster, and adapt the number of clusters to the complexity of data. In addition, DPM-BLRM incorporates the prior knowledge of LTI systems to deal with the possible large variance of model parameters estimation when the collected data is short or has low signal-to-noise ratio, where the carrier of prior knowledge is kernel matrix. Then Markov chain Monte Carlo (MCMC) method is used for Bayesian inference for the DPM-BLRM. The simulation results illustrate the efficiency of the proposed method.

关键词： LTI system clustering Dirichlet process kernel-based regularization method

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A Family of Hyper-parameter Estimators for Regularized Linear System Identification 62

A Family of Hyper-parameter Estimators for Regularized Linea...

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62nd IEEE Conference on Decision and Control (CDC)

作者： Zhang, Meng Chen, Tianshi Mu, Biqiang Chinese Acad Sci Acad Math & Syst Sci Inst Syst Sci Key Lab Syst & Control CAS Beijing 100190 Peoples R China Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Peoples R China Chinese Univ Hong Kong Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China

ISBN: (纸本)9798350301243

Hyper-parameter estimation is one of the fundamental issues for kernel-based regularized system identification methods. Empirical Bayes (EB) estimator and Stein's unbiased risk estimator (SURE) are two popular hyper-parameter estimators, but they both have advantages and disadvantages. Specifically, EB is not asymptotically optimal in the mean squared error (MSE) sense but SURE is, while SURE is more sensitive to ill-conditioned regression matrix but EB is more robust. In this paper, to find a better estimator by combining their strength and mitigating their weakness, we propose a family of hyper-parameter estimators by linking EB and SURE estimators together through an index. The finite sample and asymptotic properties of this family of estimators have been established. The Monte Carlo simulation results show that there does exist a 'middle' hyper-parameter estimator in this family that is superior to the EB and SURE.

关键词： Linear system identification kernel-based regularization method hyper-parameter estimator empirical Bayes estimator Stein's unbiased risk estimator

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An Efficient Implementation for Regularized Frequency Response Function and Transient Estimation 20

An Efficient Implementation for Regularized Frequency Respon...

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20th IFAC Symposium on System Identification (SYSID)

作者： Xu, Yu Fang, Xiaozhu Mu, Biqiang Chen, Tianshi Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Peoples R China Chinese Acad Sci Key Lab Syst & Control Inst Syst Sci Acad Math & Syst Sci Beijing 100190 Peoples R China

In this paper, we propose an efficient implementation for the kernel-based regularized frequency response function (FRF) and transient estimation. In particular, we show that when the diagonal correlated (DC) kernel is used, the output kernel matrix in the frequency domain has a hierarchically of-diagonal low-rank (HODLR) structure, and by exploring this structure, the FRF and transient estimates can be computed very efficiently The overall computational complexity is O(gamma(2) N-b log(2) N-b), where N-b is the number of data in the interested frequency band and gamma is the HODLR rank of the output kernel matrix that is often much smaller than N-b. The efficacy of the proposed implementation is demonstrated by numerical simulations. Copyright (c) 2024 The Authors.

关键词： kernel-based regularization method Efficient implementation HODLR matrix

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On the Input Design for kernel-based Regularized LTI System Identification: Power-constrained Inputs 56

On the Input Design for Kernel-based Regularized LTI System ...

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56th Annual IEEE Conference on Decision and Control (CDC)

作者： Mu, Biqiang Chen, Tianshi Ljung, Lennart Linkoping Univ Dept Elect Engn Div Automat Control SE-58183 Linkoping Sweden Chinese Univ Hong Kong Sch Sci & Engn Shenzhen 518172 Peoples R China

ISBN: (纸本)9781509028733

This paper considers the input design of kernelbased regularization methods for LTI system identification. We first derive the Bayesian mean squared error matrix under the Bayesian perspective, and then use some typical scalar measures (e.g., the A-optimality, D-optimality, and E-optimality) as optimization criteria for the input design problem. Instead of directly solving the nonconvex optimization problem, we propose a two-step procedure. The first step is to solve a convex optimization and the second one is to determine the inverse image of a quadratic map. Both of these two steps can be solved efficiently by the proposed method and hence all the globally optimal inputs are found. In particular, we show that for some kernels, the optimal input under the D-optimality has an explicit expression.

关键词： Input design Bayesian mean squared error matrix kernel-based regularization method system identification convex optimization quadratic map

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On kernel design for regularized non-causal system identification☆

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AUTOMATICA 2024年 159卷

作者： Fang, Xiaozhu Chen, Tianshi Chinese Univ Hong Kong Shenzhen Res Inst Big Data Sch Data Sci Shenzhen 518172 Peoples R China

Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its application in the non-causal system identification, and the key issue lies in the design and analysis of kernels for non-causal systems. In this paper, we develop systematic ways to deal with this issue. In particular, we first introduce the guidelines for kernel design and then extend the system theoretic framework to design the so-called non-causal simulation-induced (NCSI) kernel, and we also study its structural properties, including stability and semiseparability. Finally, we consider some special cases of the NCSI kernel and show their advantage over the existing kernels through numerical simulations. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Non -causal system identification kernel-based regularization method kernel design

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kernel-based regularized iterative learning control of repetitive linear time-varying systems

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AUTOMATICA 2023年第1期154卷

作者： Yu, Xian Fang, Xiaozhu Mu, Biqiang Chen, Tianshi Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Peoples R China Chinese Univ Hong Kong Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Chinese Acad Sci Inst Syst Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance. & COPY;2023 Elsevier Ltd. All rights reserved.

关键词： Data-driven iterative learning control kernel-based regularization method Repetitive linear time-varying systems

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An Efficient Implementation for Regularized Frequency Response Function and Transient Estimation

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IFAC-PapersOnLine 2024年第15期58卷 127-132页

作者： Yu Xu Xiaozhu Fang Biqiang Mu Tianshi Chen School of Data Science The Chinese University of Hong Kong Shenzhen 518172 China Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper, we propose an efficient implementation for the kernel-based regularized frequency response function (FRF) and transient estimation. In particular, we show that when the diagonal correlated (DC) kernel is used, the output kernel matrix in the frequency domain has a hierarchically of-diagonal low-rank (HODLR) structure, and by exploring this structure, the FRF and transient estimates can be computed very efficiently The overall computational complexity is O ( y 2 N b ) log 2 N b ), where N b is the number of data in the interested frequency band and 7 is the HODLR rank of the output kernel matrix that is often much smaller than N&. The efficacy of the proposed implementation is demonstrated by numerical simulations.

关键词： kernel-based regularization method Efficient implementation HODLR matrix

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