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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 subject to 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: 354 Thanks: 7 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 opensource 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  
Newbie Joined: Jun 2011 Posts: 2 Thanks: 0  Re: optimal control ODE existance problem Quote:
 
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 optimalcontrol 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 FilippovCesari existence theorem  you might find what you're looking for in this? 

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