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

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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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Modeling reasons for minimizing the distance between parameters

In system identification, when new parameters are calculated, is there any reason for the parameters to be close to the original parameters ?
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Estimate Beam and Ball Problem System Parameters

I'm trying to estimate the parameters of beam and ball problem model. In the problem we have output as ball position and input as gear rotation angle. The issue that i want to ask is that our ...
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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 ...
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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 ...
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Explain the existence of limit in Persistence Excitation — mostly zero and non-existent?

Definitions Persistence Excitation on page 121 here or shortly here and here. A signal is PE if this limit exists $$r_u(\tau)=\lim_{N\rightarrow\infty}\frac 1 N \sum_{t=1}^{N} ...