Recursive State-Space Identification of Non-Uniformly Sampled-Data Systems Using QR Decomposition

A recursive least-squares (LS) state-space identification method based on the QR decomposition is proposed for non-uniformly sampled-data systems. Both cases of measuring all states and only the output(s) are considered for model identification. For the case of state measurement, a QR decomposition-based recursive LS (QRD-RLS) identification algorithm is given to estimate the state matrices. For the case of only output measurement, another identification algorithm is developed by combining the QRD-RLS approach with a hierarchical identification strategy. Both algorithms can guarantee fast convergence rate with low computation complexity. An illustrative example is shown to demonstrate the effectiveness of the proposed methods

Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on JUL 4 2019, available online: http://www.tandfonline.com/10.1080/03081079.2019.1608984[EN] The main goal of this contribution is to introduce a new procedure in order to analyse properly SISO dual-rate systems (DRS) and to provide straightforward answers to some common general questions about this kind of systems. Frequency response analysis based on DRS lifting modelling can lead to interesting results about stability margins or performance prediction. As a novelty, it is explained how to understand DRS frequency response and how to handle it for an easy computation of magnitude and phase margins keeping classical frequency domain methods. There are also some repetitive questions about DRS that can be analysed and answered properly using the results from this contribution: what the optimum relation between sampling periods is or what effects does delay have in a DRS. Every step is illustrated with examples that should clarify the understanding of the text.Salt Llobregat, JJ.; Alcaina-Acosta, JJ. (2019). Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis. International Journal of General Systems. 48(5):554-574. https://doi.org/10.1080/03081079.2019.1608984S55457448

Fast bias-constrained optimal FIR filtering for time-invariant state space models

This paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias-constrained optimal finite impulse response filtering algorithm for linear discrete time-invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite-horizon and full-horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade-off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full-horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate

Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods

Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle

This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm

Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example

Parameter and State Estimator for State Space Models

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective

モーションコントロールへの応用のためのカルマンフィルタに関する研究 : デュアルレート・時間遅延補償・パラメータ推定

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 堀 洋一, 東京大学教授 大崎 博之, 東京大学教授 古関 隆章, 東京大学教授 久保田 孝, 東京大学客員准教授 坂井 真一郎, 東京大学准教授 藤本 博志University of Tokyo(東京大学