Nonlinear Data Fitting for ODE

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Chia-Hung Tsai
Chia-Hung Tsai 2011-6-21
Hello,
I have an ODE: dx(t,u)/dt = -k*x + beta*u^n/(a^n+u^n) with u being a step function and x(0,0)=0
where t and u are independent variables; k, beta, n and a are the parameters I am going to tune.
I have data for (t,u,x), and I want to find the parameter values that can minimize the error. I have been looking for information on this, but the dx/dt term seems unusual in data fitting. The cases I found all have an explicit function of x and then data fitting was carried out. Could anybody shed some light here?
Thanks!
  2 个评论
Walter Roberson
Walter Roberson 2011-6-21
Please write it out in full functional form. For example is it x(t) or is it x(t,u) ?
Walter Roberson
Walter Roberson 2011-6-21
Note: Maple says that
diff(x(t, u), t) = -k*x(t, u)+beta*u^n/(a^n+u^n)
is not enough information to go on for a solution... it needs at least one more criteria.
(When I try x(0,0)=0 it says there is no solution.)

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回答（1 个）

Rajiv Singh
Rajiv Singh 2011-6-22
See ODE parameter estimation functionality (aka nonlinear grey box modeling) of System Identification Toolbox. Some links:
http://www.mathworks.com/help/toolbox/ident/ug/bqs6lf8.html
In: http://www.mathworks.com/products/sysid/demos.html,
see: "Tutorials on Nonlinear Grey Box Model Identification"
HTH.

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