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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.

System Identification is an interconnected area of theory and engineering. Lennart Ljung is a key figure and the system identification in his words below. Other prominent figures are Bode, Nyquist, Nichols and Kalman [1].

"System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications." [2]

References

  1. "System Identification without Lennart Ljung: what would have been different?" article by Michel Gevers here.

  2. "Perspectives on System Identification" article here by Lennart Ljung.

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How to identify all the right circular cones passing through six arbitrary points

I have this interesting question. Given $6$ arbitrary points, I want to identify all the possible circular cones passing through them. The equation of a right circular cone whose vertex is at $\mathbf{r_0}$ and whose axis is along the unit vector…
Money Management Skills
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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 design is more like "state space model"-based control…
euraad
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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{bmatrix} u [ k ] & u [ k + 1 ] & \dots & \dots &…
euraad
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Who is Ho in the Ho-Kalman algorithm?

It is mentioned in the following article https://cacm.acm.org/news/210107-in-memoriam-rudolf-kalman-19302016/fulltext that (with attribution which I suspect is wrong) He also worked with Yu-Chi Ho on the minimal realization problem, resulting in…
davyjones
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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 stable, non-linear and dynamic. The input/output…
Martin G
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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 SISO models, $m = l = 1$. Create hankel matrices…
euraad
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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 $f(\bullet;\alpha,\beta): [0,+ \infty) \rightarrow R$…
Juan
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Identifying an ellipsoid from $9$ planes that are tangent to it

The algebraic (implicit) equation of an ellipsoid is $ (r - C)^T Q (r - C) = 1 $ where $ r = [x, y, z]^T $ is a point on the ellipsoid surface, and $ C = [C_x, C_y, C_z]^T $ is the center of the ellipsoid. $Q$ is a $3 \times 3$ symmetric, positive…
Money Management Skills
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How to optimize the parameter values?

Let us assume that there is the number of infectious individuals, $I(t)$, where $t=1, 2, \ldots, T$ is time. We want to take into account the restrictive measures that affect the infection probability. We introduced into a compartmental model, a…
Nick
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Improving system identification results?

I'm performing system identification of the lateral closed-loop dynamics of a quadrotor. My model receives a setpoint and should return position and acceleration. I've proposed a second order model of the type, see equations, and solved it with…
benr
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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} Set $z= \begin{bmatrix} x^2 \\ ux \\ u^2…
Betelgeuse
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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 gives me a matrix $A$ and a vector $b$. For the…
peter
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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 arrive at the original equation. To do…
Martin
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Under what condition(s) is a linear differential delay system "weakly controllable"?

I am trying to understand the conditions under which the parameters of a linear differential delay system are identifiable. I am reading this 2002 paper by Belkoura and Orlov: Identifiability analysis of linear time-delay systems. The following is…
j_manson
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