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**Statistical Decision Theory in Adaptive Control Systems by Yoshikazu Sawaragi, Yoshfumi Sunahara and Takayoshi Nakamizo**

# Statistical Decision Theory in Adaptive Control Systems by Yoshikazu Sawaragi, Yoshfumi Sunahara and Takayoshi Nakamizo

## Overview

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;

methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and

methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.
As a result, the book represents a blend of new methods in general computational analysis,

and specific, but also generic, techniques for study of systems theory ant its particular

branches, such as optimal filtering and information compression.

- Best operator approximation,

- Non-Lagrange interpolation,

- Generic Karhunen-Loevetransform

- Generalised low-rank matrix approximation

- Optimal data compression

- Optimal nonlinear filtering

methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and

methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.

### Read also

**An Introduction to Group Representation Theory**

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation…

and specific, but also generic, techniques for study of systems theory ant its particular

branches, such as optimal filtering and information compression.

- Best operator approximation,

- Non-Lagrange interpolation,

- Generic Karhunen-Loevetransform

- Generalised low-rank matrix approximation

- Optimal data compression

- Optimal nonlinear filtering