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<div dir="ltr">Markus:<br>
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<div>Thanks for telling me more about your model. I am curious and like to know more about it. </div>
<div>My understanding is that you do have </div>
<div>1) a network (edges and nodes)</div>
<div>2) components (math equations over each edge):</div>
<div> dx / dt = A * x + B * input <br>
output = C * x + D * input<br>
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<div>It seems you must solve this problem in sequence, i.e., solving edge1 to get output1. Then proceed to edge 2:</div>
<div>input2 = TF*output1, and solve </div>
<div> dx2 / dt = A * x2 + B * input2<br>
output2 = C * x2 + D * input2<br>
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<div>Here I use a simple network </div>
<div>edge1 -> node1 -> edge2.</div>
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<div>Am I correct?</div>
<div>Hong</div>
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<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thank you very much both Hong and Matt for your answers!<br>
<br>
I have looked at the examples and I am still in the middle of figuring out how the concept of network in my application differs from the concept in the examples.<br>
It is sure that this will take me a while, especially since I am a beginner.<br>
<br>
No need to take further care of my question now! I will come back later, once I am more knowledgeable.<br>
At the moment I don’t have much more than an intuition,<br>
and it tells me that it makes probably no sense to consider DMNetwork or any kind of DM for that matter.<br>
I think the bottom line is that, despite the fact that the application has very much a network character, this is a quite different kind of network.<br>
<br>
Thanks again,<br>
Markus<br>
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Appendix:<br>
--------------<br>
<br>
Nevertheless, since Hong asked about a more precise definition, and for the sake of “completeness”, I will elaborate more (just in case you want to know):<br>
<br>
Yes definitely, the problem I am dealing with can be seen as nodes connected by structures of topological dimension one (i.e. edges).<br>
<br>
The nodes always come in “in/out" pairs and one such pair is referred to as a port.<br>
<br>
Every edge (i.e. component) represents a transfer function `TF`, i.e. `OUTPUT(s) = TF(s) * INPUT(s)`, where `s` represents a complex frequency (Laplace transform).<br>
This transfer function is rational, i.e.<br>
`TF(s) = numer(s) / denom(s)`,<br>
which means it is equivalent to a linear ODE of order `n`, where `n` is the order of the polynomial `denom`.<br>
Note that this makes an edge a directed interconnection element! (INPUT --> OUTPUT is a causal relationship)<br>
<br>
This ODE of order `n` can be rewritten as a system of first-order ODEs.<br>
There are infinitely many ways to do so, but a straightforward choice is 'controllable canonical form'.<br>
<br>
Hence, *each* edge is represented by a 4-tuple of real-valued matrices (A, B, C, D).<br>
A in R^{n x n} (R stands for real numbers)<br>
B in R^{n x 1} (1 -> single input)<br>
C in R^{1 x n} (1-> single output)<br>
D in R^{1 x 1} (dito)<br>
<br>
The transfer function has the same input-output dynamics as the system<br>
dx / dt = A * x + B * input<br>
output = C * x + D * input<br>
The vector `x in R^n` is the local state (i.e. local to a particular edge / transfer function).<br>
<br>
Looking at one node, the outputs of all edges which are connected to that node with their output end are summed together.<br>
This sum is then fed as the input to all edges which are connected to that node with their input end.<br>
<br>
It is the ultimate goal to assemble a matrix `A_global` which is right-multiplied by a global state vector `x_global`.<br>
This matrix is built by appending A matrices of all edges in a block-diagonal way.<br>
Matrices B, C, D of all edges are necessary to add off-diagonal entries accounting for the interconnection of components (i.e. edges) (cf. paragraph above).</blockquote>
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