Mathematics

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.

89 questions
6
votes
2 answers

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…
user948761
4
votes
2 answers

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
  • 659
4
votes
1 answer

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
  • 3,082
4
votes
0 answers

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 & \dots…
euraad
  • 3,082
3
votes
0 answers

Find the center of the ellipse given its semi-axes and orientations and two points that lie on it

Suppose you are given the two semi-axes $ a, b$ , with $ a \gt b $ of an ellipse, as well as the angle $\theta$ the major axis makes with the positive $x$ axis. In addition, you are given two points $P_1(x_1, y_1), P_2(x_2,y_2)$ that lie on the…
user948761
3
votes
1 answer

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
  • 319
  • 1
  • 10
3
votes
0 answers

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
  • 3,082
2
votes
0 answers

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
  • 41
  • 4
2
votes
2 answers

Calculate the rank of a matrix expression

I'm studying discrete-time LTI systems and state estimators for them. Recently, I studied this paper. I am facing a matrix rank calculation problem and having trouble solving it. I will provide more details below and would appreciate any help.…
apa
  • 83
2
votes
1 answer

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…
user948761
2
votes
0 answers

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
  • 1,259
2
votes
1 answer

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
  • 33
2
votes
1 answer

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 $z= \begin{bmatrix} x^2 \\ ux \\ u^2 \end{bmatrix}$…
Betelgeuse
  • 482
2
votes
0 answers

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
  • 21
1
2 3 4 5 6