My Math Forum optimal control ODE existance problem

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 June 10th, 2011, 11:37 AM #1 Newbie   Joined: Jun 2011 Posts: 2 Thanks: 0 optimal control ODE existance problem I'm doing some researches in optimal control problems and stuck with ODE existence problem. Optimal control problem is to minimise the cost of control represented by functional $J(u)= \int_0^Tf^0(x(t),u(t),t)dt \to \min$ subject to $\dot x= f(x,u,t)$ $x(0)= x_0$ In ordinary cases unique solution of Cauchy problem exists if f(x,t) is continuous and continuously differentiable with respect to x. In case of optimal control we got u(t) which is piecewise continuous function so there is no continuity for f(x) so ordinary case theorems can't be used. And the question is: does anybody know how existence problem is solved in optimal control theory?
 June 11th, 2011, 04:44 PM #2 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 344 Thanks: 6 Math Focus: primes of course Re: optimal control ODE existance problem in case this info is of use, searching Google groups leads to: http://groups.google.com/group/psopt...-group?lnk=srg, which seems to be tied to open-source solve software. There is a similar sounding software (PROPT) I see at http://tomdyn.com/matlab_optimal_control_examples.html. Lastly, there is another called ACADO, see http://www.acadotoolkit.org/features.php. Some interact with MATLAB, others in C++. I do not otherwise have time to reply, sorry.
June 11th, 2011, 09:15 PM   #3
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Re: optimal control ODE existance problem

Quote:
 Originally Posted by billymac00 in case this info is of use, searching Google groups leads to: http://groups.google.com/group/psopt...-group?lnk=srg, which seems to be tied to open-source solve software. There is a similar sounding software (PROPT) I see at http://tomdyn.com/matlab_optimal_control_examples.html. Lastly, there is another called ACADO, see http://www.acadotoolkit.org/features.php. Some interact with MATLAB, others in C++. I do not otherwise have time to reply, sorry.
Not really what I was looking for. I need theorem(s) which would give me solution of existence and uniqueness problem, not a software. But thanks for reply.

 June 18th, 2011, 10:02 AM #4 Newbie   Joined: Dec 2008 From: Copenhagen, Denmark Posts: 29 Thanks: 0 Re: optimal control ODE existance problem Hey, I took a course on optimal-control theory about a year ago - but I don't think we went too deep into existence proofs. Anyway, I looked through the course material and came upon a theorem called Filippov-Cesari existence theorem - you might find what you're looking for in this?

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