Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [system-identification]

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

0
votes
0answers
20 views

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 ...
0
votes
0answers
23 views

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 ...
0
votes
0answers
35 views

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 ...
0
votes
0answers
22 views

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 ...
0
votes
0answers
12 views

Recursive QR-factorisation for N4SID - What does this equation mean?

I was reading a paper about recursive subspace identification, where they are using N4SID-algorithm with some extantion for the recursive method. http://www.iaescore.com/journals/index.php/IJEECS/...
0
votes
2answers
62 views

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 ...
-1
votes
1answer
43 views

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 ...
1
vote
0answers
37 views

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 ...
1
vote
1answer
71 views

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 ...
2
votes
0answers
44 views

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 ...
0
votes
0answers
85 views

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 ...
1
vote
0answers
50 views

How to derive a recursive version of a regularised cost function

I am to derive a recursive version of the following cost function and examine for which choice of D can we have a estimator windup $V(\theta) = \frac{1}{2}\sum_{t=1}^n(y(t)-\phi(t)^T\theta)^2 + \...
2
votes
1answer
75 views

System identification of a resonant system

I want to write a matlab script that would identify a system from it's inputs and outputs. I have so far had good results with simple systems, but with this slightly more complex one I'm not able to ...
0
votes
0answers
49 views

How to estimate the parameters of a nonlinear function?

I have the function: \begin{equation} f(x) = \sum\limits_{i=1}^{n} a_i \cdot x^{b_i} \cdot e^{-c_i \cdot x} \end{equation} I need to find some parameters: \begin{equation} \begin{array}{ll} {\small \...
1
vote
0answers
16 views

Grey-box system ID for a set of DAEs

I have a system of 1st order odes given by $$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$ They are constrained by an algebraic equation ...
0
votes
1answer
33 views

Identification or characterisation of time-varying parameter of a first order ODE

I have a first order ode given by $$\dot{x}(t) = \alpha f(x,t) + \beta u(t)$$ where $\left(\alpha,\beta\right)\in \mathbb{R}$ are known constants (i.e. parameters). Starting from a rich set of ...
0
votes
1answer
34 views

Identification of part of RHS of a standard ODE from input-output simulation data

From first principles, I know that the best reduced-order mathematical model that describes my complicated physical system is $$\dot{x}(t) = \alpha f(u,t) + \beta u(t)$$ where $\left(\alpha,\beta\...
1
vote
1answer
195 views

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 ...
0
votes
1answer
30 views

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 ...
4
votes
1answer
383 views

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 ...
1
vote
1answer
132 views

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 ...
0
votes
1answer
52 views

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 ...
1
vote
0answers
31 views

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 ...
0
votes
1answer
35 views

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 ...
0
votes
1answer
71 views

How do I find the noise for ARMAX model - System identification

A discrete transfer function can be described like this: $$ y[k] = \frac{B(q^{-1})}{F(q^{-1})}u[k]$$ Where can be a polynomal expression: $$B(q^{-1}) = b_0+ b_1q^{-1} + b_2q^{-2} + b_3q^{-3} + \dots ...
2
votes
0answers
210 views

Estimate a state space model by using Singular Value Decomposition

This article is from 1989 and it contains an algorithm how to estimate a state space model from arbitrary input and output. The algorithm begin with to create two hankel matrices. $$H_1 = \begin{...
1
vote
3answers
66 views

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 ...
0
votes
0answers
47 views

How can I interpret the discrete impulse response measurement?

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 = \...
0
votes
1answer
49 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_{...
3
votes
0answers
72 views

Identify a state space model from measured inputs and outputs

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 ...
0
votes
2answers
38 views

How to interpret “first r columns” at a matrix?

I'm doing oblique projections of matrices $A \in \Re^{pxj}, B \in \Re^{qxj}, C \in \Re^{rxj}$. The formula look like this: $$A/_{B}C = A(C^T \space\space\space\space B^T).[(\frac{CC^T}{BC^T} \space\...
0
votes
2answers
740 views

How can I use qr() in MATLAB to compute LQ - Decomposition?

I want to compute this: $$\begin{bmatrix} U\\ Y \end{bmatrix} = \begin{bmatrix} L_{11} &0 \\ L_{21} & L_{22} \end{bmatrix}\begin{bmatrix} Q_1\\ Q_2 \end{bmatrix}$$ Is this matlab command ...
0
votes
1answer
164 views

how to measure the fluctuation of data used for fitting a curve?

Given a series of data points that are used to fit a smooth curve, how to measure the fluctuation of the data?
1
vote
1answer
160 views

Some advice about system identification - State space or transfer functions?

I'm reading a book about mathematical modelling of dynamic linear(in theory) systems. As I know, measure simulation data and create a model of the system, is much better and gives a more exact ...
0
votes
0answers
33 views

Creating an ARMAX model - Do I need a impulse response?

I'm going to create an ARMAX model: $$y_k = -a_1y_{k-1} - \dots - a_ny_{k-n} + b_1u_{k-1} + \dots + b_nu_{k-n} = + w_k + c_1w_{k-1} + \dots + c_nw_{k-n}$$ According to my book. I need to find $y_{k}$...
0
votes
1answer
33 views

Regularize gradient matrix in order to preserve approximator stability.

I have an optimization problem, where I attempt to identify an unknown system. I usa a linear, discrete function approximator, say $$ x_{k+1} = Ax_k. $$ The method of optimization is a gradient ...
0
votes
2answers
133 views

Adaptive Control + Robust Control - Does it work?

I have a qurius question! Is it possible to design a robust controller for a system by using algoritms and system identification, which are adaptive control + robust control? I know there is a lot of ...
1
vote
0answers
46 views

Finding $A$ for Ax=B with x and B being matrices

I have a simple system which practically follows $Ax=B$, where x is input, B is output and $A$ are parameters. I have set of $k$ experiments data, so $x$ is actually $N$ by $k$, and $B$ is $M$ by $k$...
0
votes
0answers
54 views

How to solve inverse problem for a system of ODEs

Please, suggests a couple of not complicated textbooks regarding the inverse problem for ODE systems (say, Lotka-Volterra predator-prey system). Namely, I would like to know how to recover parameters ...
9
votes
2answers
5k views

What Is Spectral Leakage?

Can someone, please, explain in simple words what spectral leakage is ? I am interested in the case where a window is used to reduce the truncation error of a Fourier transform of a finite signal. ...
0
votes
0answers
35 views

Isolation of parameter values of neural network

In Section 1 of Structural identifiability of generalized constraint neural network models for nonlinear regression by Yang et al, the authors have defined structural identifiability on the second ...
1
vote
0answers
34 views

How to derive stochastic properties for a filtered signal

I am currently busy with least cost system identification developed by Michel Gevers. For this purpose, I started with the following paper: "Design of least costly identification experiments - The ...
1
vote
0answers
69 views

System identification of $Ax = b$

Given a system of the form $Ax = b$, I have a method to extract infinitely many combinations of $A$ and $b$ that satisfies a given $x$. Can I argue that any combination of $A$ and $b$ (such that $A^{-...
0
votes
1answer
27 views

Identify State Space Model using Expectation Maximization Method

For a simple LTI state space system, \begin{equation} \begin{aligned} x_{k+1}&=a x_k + w_k\\ y_k&=x_k +v_k \end{aligned}, \quad k=1,\dots,M \end{equation} where noises $w_k\sim N(0,Q)$ and $...
0
votes
1answer
85 views

Properties of Injective Operator on Hilbert Space

I am new to functional analysis and have the following issue: Given an infinite dimensional Hilbert space $H$ and an operator $f: H \times \Omega \to H$, where $\Omega$ is some finite dimensional ...
0
votes
1answer
79 views

What is the name of this formula??

Let formula_a = lambda array: sum(array) / len(array). We may rename this formula to be average or ...
2
votes
1answer
85 views

Linear Map of an ellipsoid in $\mathbb{R}^N$ into another ellipsoid in $\mathbb{R}^n$, with $n<N$

Starting from the closed set describing an ellipsoid in $\mathbb{R}^N$: $$\Omega_x = \{ x \in \mathbb{R}^N : (x-x_0)^T\Sigma_x^{-1}(x-x_0) \leq \varepsilon^2 \}$$ where $\Sigma_x \in \mathbb{R}^{N\...
0
votes
0answers
41 views

Identification of non-linear functions:polynomial+exponential

Is there a way to perform a non linear least square to identify the following function: $$\alpha_2\cdot x^2 + \alpha_1\cdot x + \alpha_0 + \beta e^{\frac{\gamma}{x}}=Y$$ I aim at identifying the ...
1
vote
0answers
67 views

Support of a Random Variable and Linear Subspaces in $\mathbb{R}^d$

I am reading a Text about Single Index Models where a theorem is given for the identification in case all covariates are continuous. The theorem states these four conditions: $G$ is differentiable ...
0
votes
1answer
53 views

How to treat non-identifiable states in Kalman filtering/dynamic linear models?

Let $x_t = G_tx_{t-1}+\omega_t$ with $\omega_t \sim \mathrm{N}(\mathbf{0}, \mathbf{W}_t)$ be a state equation and $y_t = F_tx_t+\nu_t$ with $\nu_t \sim \mathrm{N}(\mathbf{0}, \mathbf{V}_t)$ be a ...