Nonlinear Data Fitting for ODE

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!

[Walter Roberson]

Please write it out in full functional form. For example is it x(t) or is it x(t,u) ?

[Walter Roberson]

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.)

Answer 1

[Rajiv Singh]

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.