Trajectory Optimization using fmincon

Hi everybody, I'm trying to run a trajectory optimization using the Optimization Toolbox of Matlab. My goal is to optimize the ascent trajectory of a launch vehicle (which is governed by two - or even one - simple dynamic equations) modulating a certain number of design variables in order to obtain, for example, the path which maximizes the payload, adding some constraints (e.g. on the maximum dynamic pressure).

My question is: the objective function and the constraints are not analytically expressed as functions of the design variables. Can I still use the functions provided (e.g. fmincon), maybe in an iterative process? How should I proceed?

Thanks for helping.

Answer 1

[Andrew Newell]

You don't have to have an explicit expression for the objective function and constraints. If you can create a function like this:

f = myfun(x,param1,param2,...)
...

which allows a vector for x, it doesn't matter how you actually solve for f. You could solve an ode, find a root, whatever. However, if there are multiple solutions for f or you can't solve for it accurately, you have a problem.

[Francesco Capuano]

Dear Andrew,

thanks for your answer. I got your tip and now I know how to proceed.