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# 状態空間モデル

フリー、正準、構造化のパラメーター化をもつ状態空間モデル、等価の ARMAX モデルおよび OE モデル

`$\begin{array}{l}\stackrel{˙}{x}\left(t\right)=Fx\left(t\right)+Gu\left(t\right)+\stackrel{˜}{K}w\left(t\right)\\ y\left(t\right)=Hx\left(t\right)+Du\left(t\right)+w\left(t\right)\\ x\left(0\right)=x0\end{array}$`

`$\begin{array}{l}x\left(kT+T\right)=Ax\left(kT\right)+Bu\left(kT\right)+Ke\left(kT\right)\\ y\left(kT\right)=Cx\left(kT\right)+Du\left(kT\right)+e\left(kT\right)\\ x\left(0\right)=x0\end{array}$`

ここで、T はサンプル時間、u(kT) は kT 時点での入力、y(kT) は kT 時点での出力です。

## アプリ

 System Identification Identify models of dynamic systems from measured data

## ライブ エディター タスク

 状態空間モデルの推定 Estimate state-space model using time or frequency data in the Live Editor

## 関数

すべて展開する

 `idss` State-space model with identifiable parameters `ssest` Estimate state-space model using time-domain or frequency-domain data `ssregest` Estimate state-space model by reduction of regularized ARX model `n4sid` Estimate state-space model using subspace method with time-domain or frequency-domain data `pem` Prediction error minimization for refining linear and nonlinear models
 `delayest` Estimate time delay (dead time) from data `findstates` Estimate initial states of model `ssform` Quick configuration of state-space model structure `init` Set or randomize initial parameter values `idpar` Create parameter for initial states and input level estimation
 `idssdata` State-space data of identified system `getpvec` Obtain model parameters and associated uncertainty data `setpvec` Modify values of model parameters `getpar` Obtain attributes such as values and bounds of linear model parameters `setpar` Set attributes such as values and bounds of linear model parameters
 `ssestOptions` Option set for `ssest` `ssregestOptions` Option set for `ssregest` `n4sidOptions` Option set for `n4sid` `findstatesOptions` Option set for `findstates`

## トピック

### 状態空間モデルの基礎

"状態空間モデル" とは、状態変数を使用し、1 つ以上の n 階微分方程式または差分方程式ではなく、一連の 1 階微分方程式または差分方程式によってシステムを記述するモデルです。

State-Space Model Estimation Methods

Choose between noniterative subspace methods, iterative methods that use prediction error minimization algorithm, and noniterative methods.

Estimate State-Space Model With Order Selection

Select a model order for a state-space model structure in the app and at the command line.

モード正準形式、コンパニオン正準形式、可観測正準形式、可制御正準形式の状態空間モデル。

Data Supported by State-Space Models

You can use time-domain and frequency-domain data that is real or complex and has single or multiple outputs.

### 状態空間モデルの推定

Estimate State-Space Models in System Identification App

Use the app to specify model configuration options and estimation options for model estimation.

Estimate State-Space Models at the Command Line

Perform black-box or structured estimation.

Estimate State-Space Models with Canonical Parameterization

Canonical parameterization represents a state-space system in a reduced parameter form where many elements of A, B and C matrices are fixed to zeros and ones. The free parameters appear in only a few of the rows and columns in state-space matrices A, B, C, D, and K. The free parameters are identifiable — they can be estimated to unique values. The remaining matrix elements are fixed to zeros and ones.

Estimate State-Space Equivalent of ARMAX and OE Models

This example shows how to estimate ARMAX and OE-form models using the state-space estimation approach.

Estimate State-Space Models with Free-Parameterization

Free Parameterization is the default; the estimation routines adjust all the parameters of the state-space matrices.

Use State-Space Estimation to Reduce Model Order

Reduce the order of a Simulink® model by linearizing the model and estimating a lower order model that retains model dynamics.

### 構造化推定、イノベーション形式

Estimate State-Space Models with Structured Parameterization

Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values. This approach is useful when you can derive state-space matrices from physical principles and provide initial parameter values based on physical insight. You can use this approach to discover what happens if you fix specific parameter values or if you free certain parameters.

Identifying State-Space Models with Separate Process and Measurement Noise Descriptions

An identified linear model is used to simulate and predict system outputs for given input and noise signals. The input signals are measured while the noise signals are only known via their statistical mean and variance. The general form of the state-space model, often associated with Kalman filtering, is an example of such a model, and is defined as:

### 状態空間モデルのオプションの設定

Supported State-Space Parameterizations

System Identification Toolbox™ software supports various parameterization combinations that determine which parameters are estimated and which parameters remain fixed to specific values.

Specifying Initial States for Iterative Estimation Algorithms

When you estimate state-space models, you can specify how the algorithm treats initial states. This information supports the estimation procedures Estimate State-Space Models in System Identification App and Estimate State-Space Models at the Command Line.