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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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Persistence of excitation and rank conditions

Assume to have a linear system of order $n$ $$ x(k+1) = Ax(k) + Bu(k) $$ which is minimal (reachable and observable) and the following trajectories $$ U=[u(1), ...,u(T)] \quad X=[x(1), ..., x(T)]. $$ ...
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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/...
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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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68 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 ...
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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 + \...
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1answer
70 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 ...
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40 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 \...
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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 ...
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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 ...
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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\...
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1answer
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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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1answer
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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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1answer
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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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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 ...
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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{...
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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 ...
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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 = \...
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1answer
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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_{...
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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 ...
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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\...
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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 ...
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140 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?
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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 ...
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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 $y_{k}$...
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1answer
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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 ...
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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 ...
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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 $k$...
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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 ...
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What Is Spectral Leakage?

can someone, please, explain in simple words what spectral leakage is ? I am intrested in the case, when a window is used to reduce the truncation error of a Fourier transform of a finit signal. ...
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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 ...
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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 ...
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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^{-...
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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 $...
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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 ...
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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 ...
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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\...
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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 ...
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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 ...
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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 ...
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Identification of real functions

this my second question, so I'm still new... thanks in advance for any help! Basically, I'm looking for some references and tools to study the following problem. Consider the following function $f(\...
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Automatic component identification/extraction of a system

This may probably be a nonsensical question, but here goes… A definition of a system could be: “a set of interacting components, which give structure and behaviour to the system”. E.g. say, a car (a ...
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Identifiability of a state space system

I'm trying to solve assignment 4E.5 from this sheet (ship steering dynamics). My question are: Do I need to perform the Laplace Transform in order to check for identifiability? The state space model ...