Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity

AbstractSince the stochastic gradient algorithm has a slower convergence rate, this letter presents a multi-innovation stochastic gradient algorithm for a class of dual-rate sampled systems with preload nonlinearity. The basic idea is to transform the dual-rate system model into an identification model which can use dual-rate data by using the polynomial transformation technique. A simulation example is provided to verify the effectiveness of the proposed method

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

© 2018 Informa UK Limited, trading as Taylor & Francis Group. This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective

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

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

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input–multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method

A Preconditioned Iteration Method for Solving Sylvester Equations

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method

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

Parameter Identification of Permanent Magnet Synchronous Motor

V rámci dizertační práce byly navrženy identifikační metody pro synchronní motor s permanentními magnety. Celá identifikace i řízení motoru probíhalo v dq souřadnicích a pro zpracovaní bylo použito prostředí Matlab Simulink spolu s realtime platformou Dspace. Práce se zaměřila na dvě hlavní odvětví identifikace a to off-line a online identifikaci. K off-line identifikaci byla použita frekvenční analýza využívající lock rotor test pro získání třech parametrů. Jedná se o příčnou a podélnou indukčnost a odpor statoru. V online metodě byly tyto parametry ještě rozšířeny o magnetický tok magnetu _f identifikovaného pomocí metody MRAS. Zbylé parametry byly opět identifikovány pomocí frekvenční analýzy, která byla upravena pro online režim a zároveň aplikována na identifikaci více složek najednou. Poslední metodou, která se v práci nachází, je Newtonova metoda, která se využívá pro odhad odporu statoru, aniž by se do motoru musel injektovat jakýkoli signál.The purpose of this dissertation is to design identification methods for identifying a permanent magnet synchronous motor. The whole identification and motor control is carried out in d-q coordinates, and the program used for processing and control was the matlab simulink, together with the real time platform DSpace. The work focuses on two main areas of identification, off-line identification and on-line identification. For offline identification the frequency analysis was used with the lock rotor test to get three main parameters. They are the quadrature and direct inductances and stator resistance. In the online mode, the identified parameters were extended to magnet flux _f identified by MRAS method. The remaining parameters were again identified by frequency analysis, which was adapted into online mode, and simultaneously applied to the identification of several part in one time. The next method is Newton method, which is used for estimating stator resistance of the motor, without the need to apply any signal.

The extended gamma distribution with regression model and applications

This paper introduces a new extension of the gamma distribution, named as a new extended gamma distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model