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What have you tried so far using GA?
like any optimization problem if you can set up your objective function to take your tunable parameters as inputs minimizing some performance metric.
Put your ODE in a function which takes a vector of inputs for the controller parameters. Calling this function for a particular set of coefficients should solve the ODE.
You should have some metric to minimize, maybe meeting some design specifications? That is for you to decide. Create a new function that minimizes the metric by calling the above ODE function. Once you have done that call GA to minimize the function for some 'x' which is a vector of all the controller parameters.
Here is an example of optimizing an ODE using patternsearch and GA, this should be a start:
