<DIV>hi dear Juan Arrieta<BR></DIV>
<DIV>i'm a MS student in aerospace, flight dynamic and control<BR></DIV>
<DIV>the problem is a 4 stage rocket that transfer a payload (a satellite) to the geo-stationary orbit.<BR>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.<BR></DIV>
<DIV>the main goal is minimizing fuel consumed or maximizing final mass of payload.<BR>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 ?!<BR></DIV>
<DIV>the most big difficulty with this problem is generating Hessian (second derivatives) analytically.</DIV>
<DIV>as the fourth stage is not as long as other stages (about 40-50 secounds) i found that one </DIV>
<DIV> </DIV>
<DIV>simple method can be this way:<BR>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.</DIV>
<DIV> </DIV>
<DIV>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..</DIV>
<DIV> </DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>how did you solve your problems with IPOPT? did you use ampl?<BR>can you help me? do you have any idea?</DIV>
<DIV> </DIV>
<DIV>anyway , thanks for your interest<BR>i hope you be successfull too</DIV>
<DIV> </DIV>
<DIV>Cheers</DIV>
<DIV>s.serpooshan</DIV>
<DIV><BR> </DIV>
<DIV> </DIV>
<DIV><BR><B><I>Juan Jose Arrieta-Camacho <jarrieta@andrew.cmu.edu></I></B> wrote:</DIV>
<BLOCKQUOTE class=replbq style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid">Hello, I'm Juan Arrieta, Larry's PhD student.<BR><BR>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.<BR><BR>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!<BR><BR>Anyway, I hope you are able to solve your optimal control problem soon.<BR><BR>Cheers,<BR><BR>--<BR>J. J. Arrieta-Camacho<BR><BR></BLOCKQUOTE><p>__________________________________________________<br>Do You Yahoo!?<br>Tired of spam? Yahoo! Mail has the best spam protection around <br>http://mail.yahoo.com