Linearization of a system of 40 Non-linear ODEs for a model and obtain ABCD state-space matrix

Hey,

I have a system of 40 non-linear ODEs. I want to find Jacobian matrix for the same. How to Linearize the model? As it contains mass-action kinetics as well as Michaelis-menten kinetics structure? Any suggestions in this regard is appreciated.

[darova]

Is it possible?

[Darshna Joshi]

The purpose is to formulate an objective function (optimization problem) from these non-linear ODEs. Is there other way to do that? @darova

[darova]

Have no idea. What kind of optimization? You are looking for some parameter values?

[Darshna Joshi]

I want to find the best values of combinations of my inputs (There are 3 inputs) that will give me the maximum output. As i have a whole non-linear differential equation model, i don't know how to proceed with that ODEs. @darova

[Paul]

@Darshna Joshi

Can you provide a bit more insight into the form of the equations? For example, are they in the form of:

xdot(t) = f(x(t))

where x and xdot are 40 x 1? Do you have an m-function that can evaluate f()? Or maybe f() has some symbolic parameters? A few more details on the form of the equations will be helpful; a small order example would be even better.