# [Coin-ipopt] Re: Optimal Control Problem?

saeed serpooshan sserpooshan at yahoo.com
Tue Mar 1 01:44:47 EST 2005

```hi dear Juan Arrieta

i'm a MS student in aerospace, flight dynamic and control

the problem is a 4 stage rocket that transfer a payload (a satellite) to the geo-stationary orbit.
after burn out of stage 3, we have a free flight (coast-phase) that reach rocket to the near of equator plane, then stage 4 is started and lead rocket to the transfer orbit that it's apogee is as far as final geo-stationary orbit.

the main goal is minimizing fuel consumed or maximizing final mass of payload.
i'm not too familiar with AMPL and usually prefer write my own code for anything.. but it seems that AMPL is too strong for these purposes ?!

the most big difficulty with this problem is generating Hessian (second derivatives) analytically.
as the fourth stage is not as long as other stages (about 40-50 secounds) i found that one

simple method can be this way:
we consider only first three stages and use a appropriate cost function to be minimized.. it works fine and it's solution must be completely near to the real optimization problem with all stages.

another method that i'm thinking about is this: if i add (define) some junction conditions at end of stages then it's possible that define relations that transfer us from stage-3 to stage-4 as a jump condition (that should be find simply with an numerical integration), but at this time, my code dos not has such feature..

i don't have much time now because i should finish this project as soon as possible but i want to continue it and finally create a general software for optimal control problems.

how did you solve your problems with IPOPT? did you use ampl?
can you help me? do you have any idea?

anyway , thanks for your interest
i hope you be successfull too

Cheers
s.serpooshan

Juan Jose Arrieta-Camacho <jarrieta at andrew.cmu.edu> wrote:
Hello, I'm Juan Arrieta, Larry's PhD student.

I'm interested to know what type of aerospace application you are applying optimal control to. I have used IPOPT in several aerospace applications, some of which are multi-stage. It sounds that you have either an interplanetary transfer (thrust-coast-thrust) or a multistage rocket.

Is the model very large? Maybe I can help you transcribing it into AMPL, or at least figuring out the fixed variables problem. As you well know, this aerospace problems can be really though!

Anyway, I hope you are able to solve your optimal control problem soon.

Cheers,

--
J. J. Arrieta-Camacho

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