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Recursive spectral analysis of natural time series based on eigenvector matrix perturbation for online applications

IET SIGNAL PROCESSING 2011年第6期5卷 515-526页

作者： Mirmomeni, M. Lucas, C. Araabi, B. N. Moshiri, B. Bidar, M. R. Univ Tehran Control & Intelligent Proc Ctr Excellence Sch Elect & Comp Engn Tehran Iran Sch Cognit Sci Inst Studies Theoret Phys & Math Tehran Iran Sharif Univ Technol Dept Math Tehran Iran

Singular spectrum analysis (SSA) is a well-studied approach in signal processing. SSA has originally been designed to extract information from short noisy chaotic time series and to enhance the signal-to-noise ratio. SSA is good for offline applications;however, many applications, such as modelling, analysis, and prediction of time-varying and non-stationary time series, demand for online analysis. This study introduces a recursive algorithm called recursive SSA as a modification to regular SSA for dynamic and online applications. The proposed method is based on eigenvector matrix perturbation approach. After recursively calculating the covariance matrix of the trajectory matrix, R-SSA updates the eigenvalues and eigenvectors for new samples by considering the effect of the new sample as perturbation in the covariance matrix and its singular value decomposition. The eigenvalues and eigenvectors adapt simultaneously to track their true values as would be calculated from the current covariance matrix. Analysis of two well-known chaotic time series: Mackey-Glass and Lorenz chaotic time series and two natural time series: Darwin sea-level pressure and Sunspot number as non-stationary processes are considered in this study to examine the performance of the proposed recursive method. The obtained results depict the power of the proposed method in online spectral analysis of non-linear time-varying systems.

关键词： natural time series eigenvalues signal-to-noise ratio recursive SSA online spectral analysis singular spectrum analysis Signal processing and detection nonlinear time-varying system Mackey-Glass chaotic time series trajectory matrix Algebra nonstationary process R-SSA eigenvector matrix perturbation covariance matrix Darwin sea-level pressure covariance matrices spectral analysis Sunspot number Signal processing theory Lorenz chaotic time series eigenvalues and eigenfunctions signal processing singular value decomposition time series recursive spectral analysis Other topics in statistics

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Lyapunov Stability Analysis of a Twisting Based Control Algorithm for systems with Unmatched Perturbations

Lyapunov Stability Analysis of a Twisting Based Control Algo...

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IEEE Conference on Decision and Control

作者： Antonio Estrada Antonio Loria Raul Santiesteban Leonid Fridman Universidad Nacional Autonoma de Mexico (UNAM) Department of Control Engineering and Robotics Engineering Faculty. C.P. 04510 Mexico D.F. LSS-SUPELEC Gif-sur-Yvette France

ISBN: (纸本)9781612848006

In this note, we present a result on stabilization of nonlinear strict-feedback systems affected by unknown perturbations when a control based on the so-called twisting algorithm, a second-order sliding mode controller, is applied. The novelty of the note relies in the stability analysis of the closed loop system. It follows along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. However, the class of systems that we deal with are discontinuous and perturbed. Although the presented analysis is aimed to perturbed second-order systems in strict feedback form, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems. An illustrative example is provided.

关键词： Computer algorithms Stability analysis Note Taking nonlinear time-varying system second order system Closed loop systems perturbation INCOMPATIBLE Lyapunov methods Instruction repertory Novelty Feedback Discontinuous Higher-order system cascades

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Optimal Reinforcement Learning for Gaussian systems 11

Optimal Reinforcement Learning for Gaussian Systems

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Annual Conference on Neural Information Processing systems

作者： Philipp Hennig Institute for Intelligent Systems Department of Empirical Inference SpemannstraBe 38 72070 Tubingen Germany

ISBN: (纸本)9781618395993

The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finite-dimensional projection gives an impression for how this result may be helpful.

关键词： Learning nonlinear time-varying system dynamics Optimal Beliefs Gauss Gaussian processes

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STABILITY ANALYSIS APPROACH TO A CLASS OF FUZZY CONTROLLED nonlinear time-varying systemS

STABILITY ANALYSIS APPROACH TO A CLASS OF FUZZY CONTROLLED N...

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International IEEE Conference Devoted to the 150-Anniversary of Alexander S Popov

作者： Precup, Radu-Emil Tomescu, Manius L. Preitl, Stefan Petriu, Emil M. Kilyeni, Stefan Barbulescu, Constantin Politehn Univ Timisoara Dept Automat & Appl Informat RO-300223 Timisoara Romania Aurel Vlaicu Univ Arad Fac Comp Sci Arad Romania Politech Univ Timisoara Timisoara Romania Univ Ottawa Sch Informat Technol & Engn Ottawa ON Canada Politechn Univ Timisoara Power Engn Dept Timisoara Romania Politech Univ Timisoara Elect & Power Engn Fac Timisoara Romania

ISBN: (纸本)9781424439676

A stability analysis approach a class of fuzzy controlled Single Input-Single Output nonlinear time-varying systems is proposed in the paper. The stability analysis is done in the sense of Lyapunov resulting in sufficient uniform asymptotic stability conditions to be used in the design of Takagi-Sugeno fuzzy logic controllers (FLCs). Use is made of quadratic positive definite Lyapunov function candidates. An illustrative example validates the stability analysis approach by the designing of the FLC to control a nonlinear plant.

关键词： Fuzzy logic controller Lyapunov function candidate Lorenz system nonlinear time-varying system

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A Generalization of Chang Transformation for Linear time-varying systems

A Generalization of Chang Transformation for Linear Time-Var...

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2010 49th IEEE Conference on Decision and Control

作者： Xiaojing Yang J. Jim Zhu School of Electrical Engineering and Computer Science Ohio University Athens OH 45701 USA

ISBN: (纸本)9781424477456

Chang transformation was introduced for decoupling the slow and fast dynamics of a singularly perturbed Linear time Invariant (LTI) system, and it was subsequently extended to Linear time-varying (LTV) systems under the slowly-varying assumption by way of frozen-time eigenvalues. This paper extends Chang transformation from slowly-varying LTV systems to LTV systems, when the singularly perturbed system has a semi-proper coefficient matrix A_(22)(t) and LTV system w(t) velence A_(22)(t)w(t) is exponentially stable. Instead of using frozen-time eigenvalues based on slowly time-varying conditions, PD-eigenvalues for LTV systems are employed to characterize the exponential stability, thereby circumventing the slowly-varying constraint. Our results provide a larger bound on epsilon, which is a gauge on the validity of the Chang transformation, in some situations than using previous techniques. We have also recast the original Chang transformation so as to provide more insight into the decoupled subsystems. The insight will be useful in subsequent investigation on estimate of the Singular Perturbation Margin (SPM) for LTV systems. An equivalence relationship has recently been established for LTI system between the SPM and the Phase Margin (PM). The new results in this paper will facilitate the development of a PM-type stability margin metric for LTV systems, and for nonlinear, time-varying systems in the future.

关键词： Linear time-varying system DECOUPLING nonlinear time-varying system singularly perturbed systems LTI exponential stability. Insight Coefficient Matrix

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Adaptive PID Controller Based on Online LSSVM Identification

Adaptive PID Controller Based on Online LSSVM Identification

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IEEE/ASME International Conference on Advanced Intelligent Mechatronics

作者： Shang Wanfeng Zhao Shengdun Shen Yajing Xi An Jiao Tong Univ Dept Mechatron Engn Xian 710049 Shaanxi Peoples R China

ISBN: (纸本)9781424424948

The paper proposes a proportional-integral-derivative (PID) controller based on least squares support vector machines (LSSVM) identifier (PID_LSSVMI). The PID parameters of the adaptive controller are adjusted by gradient information of LSSVM for online identification of nonlinear time-varying system. To illustrate the efficiency of the proposed controller, the simulation experiments are made to compare performance of three controllers, namely, PID_LSSVMI controller, classical PID controller, and PID controller based neural network. The results show that the proposed control method is effective and can achieve better

关键词： PID LSSVM identification nonlinear time-varying system

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The nonlinear time-varying response of dynamic thermal tensioning for welding-induced distortion control

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JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING-TRANSACTIONS OF THE ASME 2007年第2期129卷 333-341页

作者： Xu, Jun Li, Wei Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents a dynamic thermal tensioning method to control the welding induced distortion under production variation. The new method determines the optimal thermal tensioning parameters based on real-time distortion measurements. The Paper is focused on a systematic study on the structural response and the development of an automatic control algorithm for the dynamic thermal tensioning process. A the thermomechanical finite element model was used to study preheating effects in a gas metal arc welding process. A model predictive strategy was adopted for automatic distortion control. It has been found that the response of the dynamic thermal tensioning process is nonlinear and time varying. However, the response model can be linearized based on the superposition principle. A threshold-based control algorithm is developed and demonstrated using both simulation and experimental results.

关键词： welding induced distortion dynamic thermal tensioning twist control thin walled structure nonlinear time-varying system

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Optimizing Adaptive Control Allocation With Actuator Dynamics

Optimizing Adaptive Control Allocation With Actuator Dynamic...

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 4593-5051

作者： Johannes Tjonnas Tor Arne Johansen Department of Engineering Cybernetics Norwegian University of Science and Technology Trondheim Norway

ISBN: (纸本)9781424414970;1424414970

In this work we address the optimizing control allocation problem for an over-actuated nonlinear time-varying system with actuator dynamic where parameters affine in the actuator and effector model may be assumed unknown. Instead of optimizing the control allocation at each time instant, a dynamic approach is considered by constructing actuator reference update-laws that represent an asymptotically optimal allocation search. By using Lyapunov analysis for cascaded set-stable systems, uniform global/local asymptotic stability is guaranteed for the optimal equilibrium sets described by the system, the control allocation update-law and the adaptive update-law, if some persistance of exitation condition holds. Simulations of a scaled-model ship, manoeuvred at low-speed, demonstrate the performance of the proposed allocation scheme.

关键词： actuators low speed allocation Ship models adaptive control nonlinear time-varying system scale models

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Sufficient conditions for the convergence of open-closed-loop PID-type iterative learning control for nonlinear time-varying systems

Sufficient conditions for the convergence of open-closed-loo...

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IEEE International Conference on systems, Man and Cybernetics (SMC 03)

作者： Shou, JX Pi, DY Wang, WH Zhejiang Univ Technol Coll Informat Engn Hangzhou 310014 Peoples R China

ISBN: (纸本)0780379527

Since it was first introduced by Arimoto iterative learning control (ILC) methods have received lots of attention because of its effectiveness and briefness. In this paper, open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common as in other ILC research papers on convergence problem, sufficient condition for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for similar ILC scheme.

关键词： convergence iterative learning control nonlinear time-varying system linear operator theory

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Applying differential transformation method to parameter identification problems

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APPLIED MATHEMATICS AND COMPUTATION 2003年第2-3期139卷 491-502页

作者： Jang, MJ Wang, JS Liu, YC Far E Coll Dept Automat & Control Tainan 704 Taiwan Far E Coll Dept Mech Engn Tainan 704 Taiwan

A direct search algorithm to find the maximum likelihood estimate for parameter identification problems is proposed in this paper. The parameter identification criterion function is constructed by differential transform, and an algorithm for adjustment of the unknown parameters is selected and used to identify the parameters in such a way that the criterion function is minimized, This method has the following advantages: (1) The spectra of system model can be obtained with the unknown parameter and the initial value of state variable, therefore, the criterion function can be constructed from the above spectra. (2) The problem of singularity and sensitivity in solving traditional inverse problems can be avoided. (3) The solving process is performed in iteration and is easy realized in the numerical computation. (4) Both linear and nonlinear problems can be solved with the same process. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： parameter identification criterion function differential transform nonlinear time-varying system maximum likelihood estimation

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