Biologically motivated state space model

Discussion in 'Math' started by joeseki, Feb 25, 2012.

  1. joeseki

    Thread Starter New Member

    Feb 25, 2012
    1
    0
    I'm very rusty at my control theory.

    could someone help me derive a state space model for the following problems:

    1)
    a molecular concentration is defined to be some function u(t)
    u(t) drives some process to generate Xm(t)
    Xm(t) generates Y(t)

    2)
    a molecular concentration is defined to be u1(t)
    a 2nd molecular concentration is defined to be u2(t)
    the 1st and 2nd molecule interact in some nonlinear fashion and this resulting process generates Xm(t)
    Xm(t) generates Y(t)

    I recall seeing a very nice presentation of transcription factor model converted into State Space, but I can no longer find the link. I wish I could remember the search criteria I used the first time.

    My first guess at the state space model is as follows

    1)
    [Xm(t)] = Ax(t) + Bu(t)
    Y(t) = Cx(t) + D

    Where
    [Xm(t)] is the first order change in X(t)
    A, B, C are time invariant constants
    D is noise in measurement

    2)
    I don't know how to do this one.
     
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