# Questions tagged [system-identification]

is related to control theory, dynamic optimization and statistical methods to build mathematical models based on some measured data.

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### How can I estimate a kalman gain matrix from system identification method?

Assume that we have the input data $u$ and output data $y$ and we want to estimate a state space model $$\dot x = Ax + Bu\\ y = Cx$$ But we want also to find the kalman gain matrix $K$. I found a ...
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### A priori structural identifiability analysis of a system of ordinary differential equation using differential algebra

Consider an ordinary differential equation model of a dynamic system: $\dot{x} = f(x,u,p)$ $y = g(x,p)$ where $x$ is the n-dimensional state vector, $u$ is the r-dimensional input vector, $p$ is ...
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### Akaike's Final Prediction Error (FPE)

Considering a zero mean weak (wide-sense) stationary $p^\mathrm{th}$ order AR process $\eta(t)$, such that \begin{equation*} \eta(t) = \sum_{k=1}^p \alpha_k \eta(t-k) + \varepsilon(t),\quad \text{...
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### Parameter identifiability and collinearity

I am working on a simple differential equation model (with 8 parameters) and try to estimate the parameters regarding datas. I tried MCMC methods but the chains do not seem to converge, even after a ...
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### Is there a way to check true/false stability in a discrete transfer/state space model?

Assume that we have a discrete transfer function $H(z)$ and a discrete state space model $x(k+1) = Ax(k) + Bu(k)$. I know how to check the stability, but computing the eigenvalues from the ...
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### Batch Least squares

I need to solve in Matlab a Least squares problem, \begin{equation} \begin{bmatrix} x^2 \\ ux \\ u^2 \end{bmatrix}^T\begin{bmatrix} H_{xx} \\ 2H_{xu} \\ H_{uu} \end{bmatrix} = y \end{equation} ...
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### linear model matrix identification with least squares

I need to do a linear model identification using least squared method. My model to identify is a matrix $A$. My linear system is: $[A]_{_{n \times m}} \cdot [x]_{_{m \times 1}} = [y]_{_{n \times 1}}$ ...
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### System Identification in a Closed-loop feedback system

I have an unstable system that doesn't have a useable output when open-loop excitation is applied. Subsequently I've used a controller to control its output. I want to use the system identification ...
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### Suppose $\dot{x}=Ax$, where $A \in \mathbb{R}^{2\times2}$. Determine $A$ from the initial and final states

Two experiments were done: $x(0)= [1,1]^T$ and $x(1)=[4, -2]^T$ $x(0)= [1, 2]^T$ and $x(1)=[5, -2]^T$ How can I find the $A$ matrix? I know how to find $e^{At}$, for $t=1$, using these $2$ ...
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### How can I find the initial state vector from state space model?

Assume that we have input $u(k)\in \Re$ and output $y(k) \in \Re$ and we estimate the black box model by using subspace identification method. $$x (k+1) = Ax (k) + Bu(k)$$ $$y (k) = Cx (k)$$ If ...
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### Model reduction of estimated state space models - System identification

Assume that we have a dynamical model in form of this simple transfer function $$G(s) = \frac{1}{2s^2 + 5s + 4}$$ G = tf(1, [2 5 4]) We do a step response with ...
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### How can I reduce noise from measurement without a Kalman Filter?

I'm going to create an adaptive Model Predictive Controller (MPC). The model is a state space model. Due to noise, it's very difficult to determine the model order. I'm using subspace identification ...
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### How can I compute recursive QR-factorization?

I wonder if it's possible to find the $Q$ and $R$ matrices from this QR-equation with only compute QR at one time only: $$A = QR$$ if, the first column of $A$ got removed and then a new column got ...
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### Is there any rule of thumb when it comes to selecting control/predict horizon for MPC?

I have a simple question: Is there any rule of thumb when it comes to selecting control/predict horizon for MPC? Normaly I set control and predict horizon equals, but I have heard that's not good ...
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### sample covariance matrix

Suppose two covariance function estimators, with the same formula except for a coefficient. Then make two sample covariance matrix(SCM) from each of the functions. Why should these matrices differ in ...
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### Recommended book on “Dynamic Model Learning” related to “System Identification”?

I need to take a course on so-called "Dynamic Model Learning" related to "System Identification" + "Machine Learning stuff". But my backrgound is more on Computer Science and Electrical Engineering ...
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### Getting differential equation from Boyle's law

I'm trying to simulate pipe installation with known amount of air in Simulink and design a PI controller for it. I was able to construct equations which reflects well my real installation. My pressure ...
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### Nonlinear system identification with known model

I would like to ask for suggestions regarding system identification with known model structure, but without known parameters. The model is a model of a physical system, it can be assumed that it is ...
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### What's the point of having a reference model in Model Reference Adaptive Control?

The MRAC(or called MRAS where S = 'System') controller is called a adaptive controller. I don't know why, because it have no system identification process loop. But what's the point to having a ...
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### I can't get my Recursive Least Square algorithm work - What have I miss?

I'm want to do a recursive least square algorithm but I can't get it to work. If you don't know what recursive least square algorithm is. Well, it just ordinary least square, but it's an algorithm ...
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### How should I interprent the Recursive Least Square algorithm?

This is the recursive least square algorithm. $$\hat{\theta}(t) = \hat{\theta}(t-1) + K(t)(y(t) - \phi^T(t)\hat{\theta}(t-1)) \\ K(t) = P(t)\phi(t) \\ P(t) = (I-K(t)\phi^T(t))P(t-1)$$ As I know, I ...
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### MIT rule VS Lyapunov design - Adaptive Control

I wonder what's the difference between MIT rule and Lyapunov design when it comes to adaptive control law? As I get it, MIT rule is more like "transfer function"-based control system and Lyapunov ...
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### Structured transfer function estimation in MATLAB?

I have some input-output data for a dynamical system (input = stimulus, output = observation). Assuming that this system is linear time-invariant, I am trying to estimate a transfer function $H(s)$ of ...
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### How do I get the amplitude of a variable sine function?

Let's assume that we have a dynamical system $$G(s) = \frac{Y(s)}{U(s)}$$ And we have measure the input $u(t)$ And we have measure the output $y(t)$. Here we can see that if we increase the ...
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### Can I use least square method to estimate a Box-Jenkins model?

I have the known measurement: Noise $e(t)$, output $y(k)$, input $u(k)$. I need to find the Box-Jenkins model: $$y[k] = \frac{B(q)}{F(q)}u[k] + \frac{C(q)}{D(q)}e[k]$$ Where $B, F, C, D$ are ...
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### Estimate a transfer function from an arbitrary response?

Assume that we have a step answer which look like this: This step answer is from a difference equation. Called a discrete ODE: $$y[k] + a_1y[k - 1] + a_2y[k - 2] = b_1u[k]$$ Which can be a ...
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### Identify a transfer function from frequency data?

Assume that I want to identify a transfer function from frequency data. Assume that I have a transfer function step response which look like this: By experience, I would say that this step response ...
Assume that we have our discrete transfer function $G(e^{j\omega_k})$ where, $k = \frac{\pi k}{M} , k = 0, \dots , M$. If we want to find Markov-parameters $g_k$ from the impulse response $$g_k = \... 1answer 90 views ### How do I find L_{22} from LQ-decomposition when using Hankel matrices Assume that we have input vector y_k \in \Re^{pxN}, u_k \in \Re^{mxN}. The vectors can be interpreted as:$$u_k = (u_0 , u_1, u_2, u_3, \dots , u_{N-1})y_k = (y_0 , y_1, y_2, y_3, \dots , y_{...
I'm using subspace identification to identify a black-box state space model. To identify I follow these steps: We have measured a vector of inputs $u_k \in \Re^{m}$ and outputs $y_k \in \Re^{l}$. For ...