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IEEE Annual Conference on Decision and Control

作者： Laurent Vanbeylen Ebrahim Louarroudi Rik Pintelon Department ELEC Vrije Universiteit Brussel Pleinlaan 2 B-1050 Brussel Belgium

ISBN: (纸本)9781467357159

In the past, the Best linear Approximation (BLA) has proven to be a good tool for the identification (generation of initial estimates) of several nonlinear model structures. However, in case of high nonlinear distortion levels, the measurement time can become very high (high number of realizations M) to reduce the uncertainty of the BLA to a reasonable level. Moreover, a number of existing methods are based on C (≥2) different BLAs (corresponding to C different classes of input signals). The total number of experiments is given by the product MC. In this paper, a novel approach is proposed to reduce the number of experiments to one by combining recently developed tools for linear time-varying systems and (slowly) nonstationary inputs. In particular, it will be shown how an input signal with a time-varying standard deviation (or set point) allows one to extract all corresponding BLAs in a single experiment. These BLAs can be used to generate high-quality initial estimates of nonlinear block-structures. The results are supported by numerical simulation experiments.

关键词： linear approximation system identification time varying input signal linear time-varying system simulation test Set of points measuring time Nonlinear Models Masonry construction

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A novel synchrosqueezing transform associated with linear canonical transform

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SIGNAL PROCESSING 2025年 227卷

作者： Miao, Hongxia Beijing Univ Posts & Telecommun Sch Informat & Commun Engn State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China

Synchrosqueezing transforms have aroused great attention for its ability in time-frequency energy rearranging and signal reconstruction, which are post-processing techniques of the time-frequency distribution. However, the time-frequency distributions, such as short-time Fourier transform and short-time fractional Fourier transform, cannot change the shape of the time-frequency distribution. The linear canonical transform (LCT) can simultaneously rotate and scale the time-frequency distribution, which enlarges the distance between different signal components with proper parameters. In this study, a convolution-type short-time LCT is proposed to present the time-frequency distribution of a signal, from which the signal reconstruction formula is given. Its resolutions in time and LCT domains are demonstrated, which helps to select suitable window functions. A fast implementation algorithm for the short-time LCT is provided. Further, the synchrosqueezing LCT (SLCT) transform is designed by performing synchrosqueezing technique on the short-time LCT. The SLCT inherits many properties of the LCT, and the signal reconstruction formula is obtained from the SLCT. Adaptive selections of the parameter matrix of LCT and the length of the window function are introduced, thereby enabling proper compress direction and resolution of the signal. Finally, numerical experiments are presented to verify the efficiency of the SLCT.

关键词： Synchrosqueezing transform Generalized convolution operation LCT Chirp linear time-varying system

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Discrete Quaternion Quadratic Phase Fourier Transform

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COMPLEX ANALYSIS AND OPERATOR THEORY 2025年第3期19卷 1-22页

作者： Zayed, Mohra Dar, Aamir H. Bhat, M. Younus King Khalid Univ Coll Sci Math Dept Abha 61413 Saudi Arabia Mehta Family Sch Data Sci & Artificial Intelligenc Sch Energy Sci & Engn Gauhati 781039 India Islamic Univ Sci & Technol Dept Math Sci Awantipora 192122 Kashmir India

As a novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical transform (LCT), and special affine Fourier transforms. Due to its additional degrees of freedom, QPFT performs better in applications than other time-frequency analysis methods. Recently, quaternion quadratic phase Fourier (QQPFT), an extension of the QPFT in quaternion algebra, has been derived and since received noticeable attention because of its expressiveness and grace in the analysis of multi-dimensional quaternion-valued signals and visuals. To the best of our knowledge, the discrete form of the QQPFT is undefined, making it impossible to compute the QQPFT using digital techniques. It initiated us to introduce the two-dimensional (2D) discrete quaternion quadratic phase Fourier (DQQPFT) that is analogous to the 2D discrete quaternion Fourier transform (DQFT). Some fundamental properties are obtained, including Modulation, the reconstruction formula, and the Plancherel theorem of the 2D DQQPFT. Crucially, the fast computation algorithm and convolution theorem of 2D DQQPFT, which are essential for engineering applications, are also considered. Finally, we present an application of the DQQPFT to study the two-dimensional discrete linear time-varying systems.

关键词： Discrete quaternion quadratic phase Fourier transform Convolution Fast algorithm linear time-varying system

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New smoothed-state estimation for correlated process and measurement noises

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CONTROL THEORY AND TECHNOLOGY 2025年第2期23卷 176-192页

作者： Chen, Fu-Xi Geng, Li-Hui Ninness, Brett Zhang, Yong-Li Tianjin Univ Technol & Educ Sch Automat & Elect Engn Tianjin 300222 Peoples R China Tianjin Key Lab Informat Sensing & Intelligent Con Tianjin 300222 Peoples R China Univ Newcastle Fac Engn & Built Environm Callaghan NSW 2308 Australia

This paper addresses the computational problem of fixed-interval smoothing state estimation in linear time-varying Gaussian stochastic systems. A new fixed-interval Kalman smoothing algorithm is proposed, and the corresponding form of the smoother is derived. The method is able to accommodate situations where process and measurement noises are correlated, a limitation often encountered in conventional approaches. The Kalman smoothing problem discussed in this paper can be reformulated as an equivalent constrained optimization problem, where the solution corresponds to a set of linear equations defined by a specific co-efficient matrix. Through multiple permutations, the co-efficient matrix of linear equations is transformed into a block tridiagonal form, and then both sides of the linear system are multiplied by the inverse of the co-efficient matrix. This approach is based on the transformation of linear systems described in the SPIKE algorithm and is particularly well-suited for large-scale sparse block tridiagonal matrix structures. It enables efficient, parallel, and flexible solutions while maintaining a certain degree of block diagonal dominance. Compared to directly solving block tridiagonal co-efficient matrices, this method demonstrates appreciable advantages in terms of numerical stability and computational efficiency. Consequently, the new smoothing algorithm yields a new smoother that features fewer constraints and broader applicability than traditional methods. The estimates, such as smoothed state, covariance, and cross-covariance, are essential for fields, such as system identification, navigation, guidance, and control. Finally, the effectiveness of the proposed smoothing algorithm and smoother is validated through numerical simulations.

关键词： New Kalman smoother Correlated noises Fixed interval linear time-varying system SPIKE algorithm.

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State augmentation method for multimode nonstationary vibrations of long-span bridges under extreme winds

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ENGINEERING STRUCTURES 2025年 332卷

作者： Lei, Simian Cui, Wei Patruno, Luca de Miranda, Stefano Zhao, Lin Ge, Yaojun Tongji Univ State Key Lab Disaster Reduct Civil Engn Shanghai 200092 Peoples R China Tongji Univ Coll Civil Engn Dept Bridge Engn Shanghai 200092 Peoples R China Tongji Univ Key Lab Transport Ind Bridge Wind Resistance Techn Shanghai 200092 Peoples R China Univ Bologna DICAM I-40121 Bologna Italy

Stochastic dynamic analysis frequently relies on the assumption of time independence of linear systems and the stationarity of stochastic excitations, facilitating a variety of engineering studies. Nevertheless, these assumptions may not consistently remain valid, particularly in cases of structural vibrations induced by nonstationary extreme winds, and can lead to inaccurate predictions. The excitations in these scenarios have notable nonstationary characteristics because of the unstable nature of the flow. In addition, when aeroelastic forces are considered, the combined aerodynamic-mechanical system transforms into a linear time-varying system with aerodynamic damping and stiffness that change over time. In this work, a state augmentation approach for computing the multimode vibrations of a long-span bridge under nonstationary wind conditions is presented. The methodology integrates both nonstationary turbulence-induced forces and unsteady motion-induced forces. The coupling between motion-induced forces and bridge vibrations renders the system damping and stiffness matrices both time-varying and asymmetric;this results in complex-valued modes and coupled dynamics that cannot be adequately captured by a single-degree-of-freedom (SDOF) model. The proposed multi-degree-offreedom (MDOF) approach is a stochastic calculus-based method that avoids complex modal analysis. The statistical moments of all orders for the responses of the MDOF systems are derived via Ito's formula and the stars and bars approach. Compared with existing approaches, the new approach is both reliable and efficient, demonstrating its potential for accurate and efficient analysis of nonstationary vibrations in complex engineering systems.

关键词： Nonstationary wind Multimode buffeting Moment equations linear time-varying system Ito's formula

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A modified highly precise direct integration method for a class of linear time-varying systems

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Science China(Physics,Mechanics & Astronomy) 2014年第7期57卷 1382-1389页

作者： LIU XiaoMei ZHOU Gang ZHU Shuai WANG YongHong SUN WeiRong WENG ShiLie School of Mechanical Engineering Shanghai Jiao Tong University Department of Mathematics Shanghai Jiao Tong University

It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering *** a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was *** introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration *** method attains higher precision than the common methods(***4 and power series)and high efficiency in *** numerical examples demonstrate the validity and efficiency of the method proposed.

关键词： linear time-varying system highly precise direct integration state transfer matrix Runge-Kutta method

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NORMALIZED COPRIME FACTORIZATIONS FOR linear time-varying systemS

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systemS & CONTROL LETTERS 1992年第6期18卷 455-465页

作者： RAVI, R PASCOAL, AM KHARGONEKAR, PP GE CENT RES & DEVCONTROL SYST LABSCHENECTADYNY 12301 INST SUPER TECN CAPS COMPLEX 1P-1096 LISBONPORTUGAL INST SUPER TECN DEPT ELECT ENGNP-1096 LISBONPORTUGAL UNIV MICHIGAN DEPT ELECT ENGN & COMP SCIANN ARBORMI 48109

In this paper we show that a finite dimensional linear time-varying continuous-time system admits normalized coprime factorizations if and only if it admits a stabilizable and detectable realization. We construct state-space formulas for these factorizations using the stabilizing solutions to standard Riccati differential equations. In the process. we give a simple proof that stabilizability and detectability are sufficient to ensure the existence of such solutions. Based on these results. and on recent advances in the theory of H(infinity) optimization. we present an algorithm to compute the distance between two systems in the gap metric.

关键词： linear time-varying system NORMALIZED COPRIME FACTORIZATION GAP METRIC LYAPUNOV EQUATION RICCATI EQUATION

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Sufficient Conditions on Observability Grammian for Synchronization in Arrays of Coupled linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2010年第11期55卷 2586-2590页

作者： Tuna, S. Emre Middle E Tech Univ Dept Elect & Elect Engn TR-06531 Ankara Turkey

Synchronizability of stable, output-coupled, identical, linear time-varying systems is studied. It is shown that if the observability grammian satisfies a persistence of excitation condition, then there exists a bounded, linear time-varying feedback law that yields exponential synchronization for all fixed, asymmetrical interconnections with connected graphs. Also, a weaker condition on the grammian is given for asymptotic synchronization. No assumption is made on the strength of coupling between the systems.

关键词： linear time-varying system observability grammian persistence of excitation synchronization synchronizing feedback law

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Stabilizability of linear time-varying systems

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systemS & CONTROL LETTERS 2013年第9期62卷 747-755页

作者： Anderson, Brian D. O. Ilchmann, Achim Wirth, Fabian R. Australian Natl Univ Res Sch Engn Canberra ACT 0200 Australia Natl ICT Australia NICTA Canberra ACT 2601 Australia Tech Univ Ilmenau Inst Math D-98693 Ilmenau Germany Univ Wurzburg Inst Math D-97074 Wurzburg Germany

For linear time-varying systems with bounded system matrices we discuss the problem of stabilizability by linear state feedback. For example, it is shown that complete controllability implies the existence of a feedback so that the closed-loop system is asymptotically stable. We also show that the system is completely controllable if, and only if, the Lyapunov exponent is arbitrarily assignable by a suitable feedback. For uniform exponential stabilizability and the assignability of the Bohl exponent this property is known. Also, dynamic feedback does not provide more freedom to address the stabilization problem. The unifying tools for our results are two finite (L-2) cost conditions. The distinction of exponential and uniform exponential stabilizability is then a question of whether the finite cost condition is uniform in the initial time or not. (C) 2013 Elsevier B.V. All rights reserved.

关键词： linear time-varying system Feedback stabilization Lyapunov exponent Bohl exponent Quadratic optimal control Riccati equation

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KALMAN CANONICAL DECOMPOSITION OF linear time-varying systemS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2014年第1期52卷 274-310页

作者： Jikuya, Ichiro Hodaka, Ichijo Nagoya Univ Dept Aerosp Engn Chikusa Ku Nagoya Aichi 4648603 Japan Miyazaki Univ Dept Elect & Elect Engn Miyazaki 8892192 Japan

In this paper, a Kalman canonical decomposition of finite-dimensional linear time-varying continuous-time systems is revisited. Two types of Kalman canonical decompositions are considered;one is collectively dubbed the intervalwise Kalman canonical decomposition and the other is collectively dubbed the global Kalman canonical decomposition. Each type is classified into sub-types resulting from variants of controllabilities (i.e., controllability, reachability, and influenceability) and observabilities (i.e., observability, determinability, and visibility). This paper first investigates the invariance properties of subspaces resulting from variants of controllabilities and observabilities. This paper then gives a self-contained exposition of each Kalman canonical decomposition on an interval. The main result is to prove the existence of intervals on each of which each Kalman canonical decomposition exists. Moreover, the relations among different Kalman canonical decompositions are extensively studied and the inconsistency between the works by Youla and Weiss is resolved.

关键词： linear time-varying system Kalman canonical decomposition controllability reachability influenceability observability determinability visibility minimal realization

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