Teruyo Wada

Spectral expressions of information measures of Gaussian time series and their relation to AIC and CAT

Interrelations among the spectral expressions of the information measures of Kullback-Leibler (1959) and Renyi (1961) for discrimination between two stationary Gaussian time series are discussed. The spectral expression of Fishers information rate matrix is also treated, as well as two intuitively acceptable discrimination functions. It is shown that all of them are equivalent except for scalar multiplication and are expressed by Fishers information rate matrix in the sense of their second-order Taylor series approximation. Finally, a relation between two criteria for order determination of models for time series data, namely, H. Akaikes (1974) information criterion (AIC) and the criterion of autoregressive transfer functions (CAT), is discussed in connection with these spectral expressions. >

Gain scheduled control of nonlinear systems based on the linear-model-sets identification method

We present a total method of modeling, identification and gain scheduling for nonlinear plants. To construct a gain scheduled control system, we will expect to model the nonlinear plant as a set of the linearized models at all the operating points. In this paper, we show that the linear-model-sets identification (LM-sets ID) method is a suitable method of modeling and identification of nonlinear plants for constructing gain scheduled control systems. For this purpose, we design and theoretically analyze a gain scheduled control system based on a collection of model sets obtained by the LM-sets ID method.

Modeling of nonlinear systems for linear robust control theory: Identification via linear model sets under shifts of operating points

Considering shifts of operating points of nonlinear systems, total methods of identifying linearized models and designing feedback control systems for the nonlinear systems are presented. In the methods, a set of linear models is identified, which includes the linearized models of the nonlinear system at all the points in the entire range of expected changes of the operating point. For the model set, a linear stabilizing controller is designed by linear robust control theory and it is applied to the original nonlinear system. The obtained feedback control system for the nonlinear system is valid since all the expected equilibrium states are asymptotically stable.

A spectral estimation algorithm based on minimum cross entropy method

The minimum cross entropy (MCE) spectral analysis method is able to incorporate a prior information of spectra into the spectral analysis. Applying the principle of the MCE, the authors proposed a continuous spectral estimation method (C-MCEM) for stationary time series with a prior spectrum generated by AR models under the observation of the autocorrelation values. In this paper, combining the C-MCEM with the Burg algorithm (1975), we derive a new spectral estimation algorithm where the time series data as well as a prior spectrum are utilized. Applying the proposed method to sound data, we also show the spectral estimation results.

An AR Model Identification Method using a Prior Information and Its Application to a Spectral Estimation of Speech Signal-An Extension of the Burg Method Based on the Principle of the Minimum Cross Entropy

A novel Auto Regressive (AR) model parameter estimation method is proposed, which can utilize a prior information as well as time series data, by extending the Burg method on the basis of the Minimum Cross Entropy (MCE) principle. As a practical application of the proposed method, we consider an approach to spectral estimation of speech data. In general, effectiveness of a prior information to spectral estimation results depends on the variation of speech signal. Thus we introduce an algorithm to determine the usage of a prior information, based on the divergence measure defined by the Kullback information. Finally, the estimation results for real speech data illustrate improved performance in comparison to the Burg method.