状态空间模型

具有自由、标准和结构化参数化的状态空间模型；等效 ARMAX 和输出-误差 (OE) 模型

状态空间模型使用状态变量通过一组一阶微分方程或差分方程（而非一个或多个 n 阶微分方程或差分方程）来描述系统。如果一阶差分方程组对于状态和输入变量是线性的，则该模型称为线性状态空间模型。

注意

一般来说，System Identification Toolbox™ 文档将线性状态空间模型简单地称为状态空间模型。您还可以使用灰盒和神经状态空间对象识别非线性状态空间模型。有关详细信息，请参阅Available Nonlinear Models。

线性状态空间模型结构是快速估计的理想选择，因为您只需要指定一个参数，即模型阶数 n。模型阶数是一个等于 x(t) 维度的整数，与相应线性差分方程中使用的延迟输入和输出数目有关，但不一定等于该数量。状态变量 x(t) 可以根据测量的输入/输出数目据重新构造，但它们本身在试验期间无法测量。

在连续时间下定义参数化状态空间模型通常比在离散时间下更容易，因为物理定律通常用差分方程来描述。在连续时间下，线性状态空间描述采用以下形式：

$\begin{array}{l} \dot{x} (t) = F x (t) + G u (t) + \tilde{K} w (t) \\ y (t) = H x (t) + D u (t) + w (t) \\ x (0) = x 0 \end{array}$

矩阵 F、G、H 和 D 包含具有物理意义的元素，例如材料常数。K 包含扰动矩阵。x0 指定初始状态。

您可以同时使用时域和频域数据来估计连续时间状态空间模型。

离散时间线性状态空间模型结构通常以创新形式编写，它描述噪声：

$\begin{array}{l} x (k T + T) = A x (k T) + B u (k T) + K e (k T) \\ y (k T) = C x (k T) + D u (k T) + e (k T) \\ x (0) = x 0 \end{array}$

这里，T 是采样时间，u(kT) 是 kT 时刻的输入，y(kT) 是 kT 时刻的输出。

您不能使用连续时间频域数据来估计离散时间状态空间模型。

App

系统辨识	从测量数据辨识动态系统模型

Estimate state-space model using time or frequency data in the Live Editor

`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`	使用时域或频域数据子空间方法估计状态空间模型
`era`	Estimate state-space model from impulse response data using Eigensystem Realization Algorithm (ERA) (自 R2022b 起)
`pem`	Prediction error minimization for refining linear and nonlinear models

`delayest`	根据数据估计时间延迟（死区时间）
`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 for 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

什么是状态空间模型？
状态空间模型使用状态变量通过一组一阶微分方程或差分方程（而非一个或多个 n 阶微分方程或差分方程）来描述系统。如果一阶差分方程组对于状态和输入变量是线性的，则该模型称为线性状态空间模型。
状态空间模型估计方法
在非迭代子空间方法、使用预测误差最小化算法的迭代方法和非迭代方法之间进行选择。
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.
State-Space Realizations
A state-space model can be expressed in an infinite number of realizations. Common forms, sometimes called canonical forms, include modal, companion, observable, and controllable forms.
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.

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.
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.
System Identification Using Eigensystem Realization Algorithm (ERA)
Estimate state-space model from impulse response data using Eigensystem Realization Algorithm (ERA).

Estimate State-Space Models with Structured Parameterization
Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.
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.

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.